an isotropic two-dimensional harmonic oscillator has the hamiltonian d2 d2 -h2 1 kx ky 2 1 dx2 2u dy2 2 what is the ground state wave function for this system? and the ground state energy? what is the energy of the first excited state? tell me about any degeneracy in this system
Answers
The ground state wave function and energy of the isotropic two-dimensional harmonic oscillator, the Schrödinger equation for this system.
The Schrödinger equation for a 2D isotropic harmonic oscillator is:
(E - H) Ψ(x, y) = 0
- E is the energy eigenvalue
- H is the Hamiltonian operator
- Ψ(x, y) is the wave function of the system
The Hamiltonian operator for this system is given as:
H = - (ħ^2 / (2m)) * (d^2/dx^2 + d^2/dy^2) + (1/2) * k * (x^2 + y^2)
Now, let's solve the Schrödinger equation for the ground state wave function and energy.
1. Ground State Wave Function:
In the ground state, the wave function Ψ(x, y) will be the lowest energy eigenstate. We can assume that the wave function separates into a product of two independent wave functions, one in the x-direction (Φ(x)) and one in the y-direction (Φ(y)):
Ψ(x, y) = Φ(x)Φ(y)
The ground state wave function will correspond to the lowest energy state, which is the solution to the Schrödinger equation. By applying the Hamiltonian operator to the wave function and setting it equal to the energy eigenvalue, we can solve for Φ(x) and Φ(y).
(d^2Φ(x)/dx^2) + (d^2Φ(y)/dy^2) + (2m / ħ^2) * [E - (1/2) * k * (x^2 + y^2)] * Φ(x)Φ(y) = 0
Since the equation separates into two independent variables, we can write it as:
(d^2Φ(x)/dx^2) + (2m / ħ^2) * [E_x - (1/2) * k * x^2] * Φ(x) = 0
and
(d^2Φ(y)/dy^2) + (2m / ħ^2) * [E_y - (1/2) * k * y^2] * Φ(y) = 0
Here, E_x and E_y represent the energies in the x-direction and y-direction, respectively.
The solutions to these equations are Hermite polynomials for the x-direction and y-direction. The ground state wave function will correspond to the lowest energy state, which is the solution with the lowest energy eigenvalue.
2. Ground State Energy:
The ground state energy is the lowest energy eigenvalue obtained from the solution of the Schrödinger equation for the ground state wave function.
3. Energy of the First Excited State:
The first excited state energy will correspond to the next higher energy eigenvalue obtained from the solution of the Schrödinger equation.
4. Degeneracy:
The degeneracy of a system refers to the number of distinct states that have the same energy. In the case of the isotropic two-dimensional harmonic oscillator, the degeneracy arises due to the fact that multiple combinations of quantum numbers (n_x, n_y) can yield the same energy. The degeneracy is related to the possible values of the quantum numbers and is specific to the system's energy levels.
To obtain the exact ground state wave function, ground state energy, and energy of the first excited state, further mathematical calculations are required using the specific form of the Hamiltonian and solving the corresponding differential equations.
Learn more about wave function here
https://brainly.com/question/33260550
#SPJ11
Related Questions
Johnny is drinking a glass of orange juice when he is informed that orange juice is acidic. He begins to panic, thinking his blood will soon turn to acid. Why should he not be worried?.
Answers
Johnny needs not to be worried because blood contains buffering agents which resist changes in pH.
What is blood?Blood is defined as the fluid of the circulatory system that is made of various cells and plasma the travels through the body in veins and arteries. The cells found in the blood include the following:
White blood cells (monocytes, lymphocytes, neutrophils, eosinophils, basophils, and macrophages),Red blood cells (erythrocytes), and Platelets.At the normal healthy state of an individual, the pH of the blood is kept constant at 7.35 to 7.45. This is because, the buffering agents found in the blood such as carbonic acid and bicarbonate anion helps in the maintenance of the blood pH.
Learn more about blood vessels here:
https://brainly.com/question/25149738
#SPJ1
When the Sun rises, it is located in the constellation Gemini. When the Sun sets later that same day, it will be:
Answers
Kirchhoff's current law states that the current arriving at any junction point in a circuit is equal to the current leaving that junction O True O False
Answers
The answer is True. The conservation of charge, or Kirchhoff's current law, stipulates that the total current entering and leaving a junction in an electrical circuit must equal each other.
Kirchhoff's current law asserts that the algebraic sum of currents at any junction point (or node) in an electrical circuit is always zero, often known as the junction rule or the first law. This law is founded on the idea that charge cannot be created or destroyed, which is known as the conservation of charge. Any current that enters a junction must therefore be balanced by an equivalent current that exits the junction. By using current relationships at various nodes, this law serves as the basis for understanding and resolving complex electrical circuits. It is a cornerstone of circuit analysis and is frequently applied in physics and electrical engineering.
The algebraic sum of currents entering every junction point (or node) in an electrical circuit must match the algebraic sum of currents exiting that junction, according to Kirchhoff's current law, sometimes referred to as the junction rule or Kirchhoff's first law. Alternatively said, the total current entering a node equals the total current leaving it. This law is based on the concept of conservation of charge, which holds that electric charge can only be moved from one place to another and cannot be created or destroyed. The entire amount of charge entering a junction must match the total amount of charge exiting that junction since electrons carry charge through a circuit.
To know more about Kirchhoff's current law,
https://brainly.com/question/30394835
#SPJ4
If i took physical science in 7thgrade do i get credit for physics
Answers
Answer:
I don't think so
Explanation:
At what point of a projectile motion, acceleration and velocity are perpendicular to each other?
Answers
Answer:
At the topmost point where the velocity has only horizontal component whereas the acceleration is vertical.
Explanation:
There is only a horizontal component of velocity at the ap3x of the projectile, and acceleration is vertically downwards owing to gravitation, therefore velocity and acceleration are perpendicular to one another.
A car traveled 1,215 km West from El Paso to Dallas in 13.5 hours. What was its velocity?
A. 90m/s West
B. 90km/h
C. .09km/h West
D. 90km/h West
Answers
Answer:
D. 90km/hr due West
Explanation:
Given parameters:
Displacement = 1215km
Time = 13.5hr
Unknown:
Velocity = ?
Solution:
Velocity is the displacement divided by the time taken;
Velocity = \(\frac{displacement}{time}\) = \(\frac{1215km}{13.5hr}\) = 90km/hr
Velocity is 90km/hr due West
A student designed an experiment to show how water is recycled through the atmosphere. The steps of the experiment are shown below. Boil 500 mL of water in a beaker. Hold a hot glass plate a few inches above the beaker with a pair of tongs. Observe water droplets on the glass plate. The student did not see water dripping off the glass plate as expected because the experiment had a flaw. Which of these statements best describes a method to correct the flaw in this experiment?
Hold the glass plate closer to the beaker.
Boil the water in a pan instead of a beaker.
Take more than 500 mL of water in the beaker.
Use a cold glass plate instead of a hot glass plate.
Answers
The flaw in the experiment on water recycling is that the student did not see water dripping off the glass plate as expected. To correct this flaw, the student should use a cold glass plate instead of a hot glass plate.
The correct option to the given question is option 4.
When the student holds the hot glass plate above the beaker, the water vapor in the atmosphere will come into contact with the cold surface of the plate and condense, forming water droplets. However, if the glass plate is already hot, it will not be able to cool down the water vapor quickly enough for condensation to occur.
By using a cold glass plate, the temperature difference between the plate and the water vapor will be greater, allowing for faster condensation. This will result in water droplets forming on the glass plate and dripping off, demonstrating the process of water recycling through the atmosphere.
Therefore, the correct method to correct the flaw in this experiment is to use a cold glass plate instead of a hot glass plate. This will enable the student to observe water droplets on the glass plate as expected.
For more such questions on water visit:
https://brainly.com/question/1313076
#SPJ8
How can knowing a chemical property such as flammability help you to use a product safely?
Answers
Answer:
When a substance burns, it produces new substances during a chemical change. Therefore, whether or not a substance is flammable is a chemical property. Knowing which substances are flammable helps you to use them safely. Another chemical property is how compounds react to light
Which city has the lowest temperature and slowest speed of sound?
a. Baguio
b. Manila
c. Lipa
d. Cagayan
e. Cebu
f. Tagaytay
Answers
ITS A a AAA A A a A A A A A A A
help please.
How many days occur between a new moon and a first quarter moon?
Answers
Answer:
7 days or a week
Explanation:
what do atoms gain, lose, or share when they boned
Answers
Answer:
Explanation:
An atom losses or gains electrons to fill the outermost shell. In this process , ionic bonds are formed. Chemical bonds are formed when electrons are shared.
Which best compares radiation and conduction?
A. Both transfer thermal energy from warm objects to cooler objects.
B. Both can transfer energy through empty space.
C. Both transfer thermal energy by electromagnetic waves.
D. Both involve the transfer of energy through direct contact.
And also who likes Rick and Morty OwO
Answers
Answer:
A
Explanation:
which nuclear decay emission consists of energy only?
Answers
Answer:
Gamma radiation
Explanation:
Gamma radiation is a decay emission of pure energy.
The force as a function of displacement of a moving object is represented by the graph. How much work is done when the object moves from 0 m to 2 m?
Answers
6 joule is work done when the object moves from 0 m to 2 m
F=3N
d=2m
work done=Fd
work done=2×3
work done=6 joule
When moving an object over a distance, an external force must direct at least a portion of its force in the direction of the displacement. This is referred to as work done in physics. If the force acting along the path is constant, the amount of work can be calculated by multiplying the length of the path by the force's component. The work W is equal to the force f times the distance h to express this idea mathematically, or W = mgh. The work is W = mas if the force is applied at an angle to the displacement.
To know more about work done visit : brainly.com/question/10334435
#SPJ1
At what temperature (in Kelvin) will the diffusion coefficient for the diffusion of species A in metal B have a value of 5.68 × 10-16 m2/s, given that the values of D0 and Qd are 5.4 × 10-6 m2/s and 219 kJ/mol, respectively?
Answers
The temperature (in Kelvin) at which the diffusion coefficient for the diffusion of species A in metal B have a value of 5.68 × 10⁻¹⁶ m²/s is 1121 K.
How to find the temperatureDiffusion coefficient, species A, metal B, temperature, Kelvin, D0, Qd, and value of 5.68 × 10⁻¹⁶ m2/s.
Given that the values of D0 and Qd are 5.4 × 10-6 m2/s and 219 kJ/mol, respectively, the formula to calculate the temperature (in Kelvin) will be as follows;
D = D0exp(-Qd/RT)
Where;
D = Diffusion Coefficient = 5.68 × 10⁻¹⁶ m²/s
D₀ = Pre-exponential factor = 5.4 × 10⁻⁶ m²/s
Qd = Activation energy = 219 kJ/mol
R = Gas constant = 8.31 J/mol
KTo get the temperature in Kelvin, we can use this formula by substituting the values,
D = D₀exp(-Qd/RT)5.68 × 10-16 m²/s = 5.4 × 10⁻⁶ m²/s × exp (-219 × 10³ J/mol)/(8.31 J/mol K × T)
Simplifying the equation, exp (-Qd/RT) = 1.1111 × 10⁻⁷
Taking natural logarithms on both sides, -Qd/RT = ln (1.1111 × 10⁻⁷)
Qd/RT = -ln (1.1111 × 10⁻⁷)
Substituting the values, 219 kJ/mol/ (8.31 J/mol K × T) = -ln (1.1111 × 10⁻⁷)
Solving for T, T = 1121 K (approx)
Learn more about diffusion coefficient at
https://brainly.com/question/13256293
#SPJ11
Question 51 pts Which of the following illustrates an increase in potential energy? Group of answer choices a wind-up toy winding down an apple dropping from a tree a person climbs a set of stairs a firecracker explodes
Answers
Answer:
a person climbs a set of stairs
Explanation:
A person climbing a set of stairs increases his height, which also increases his gravitopotential energy. Gravitopotential energy increases with height as you move further away from the surface of the Earth.
A wind up toy winding down is already expending its stored up potential energy. An apple falling from a tree is already losing its gravitipotential energy. A firecracker that explodes is already using up the potential energy stored in its chemical. All these are cases where the potential energy is decreasing.
if you are at latitude 59° north of earth's equator, what is the angular distance from the northern horizon up to the north celestial pole?
Answers
If you are at latitude 59° north of the earth's equator, the angular distance from the northern horizon up to the north celestial pole will be 59 degrees.
The celestial pole is a star located at the Earth's poles. If you stand at any of Earth's poles, you will observe the North Stars directly overhead. The star is fixed in the sky's position; it neither rises nor sets. However, as you travel from the equator toward the pole, the angular distance between the star and the northern horizon increases.The angular distance from the northern horizon up to the north celestial pole is the observer's latitude. That means, for an observer located at a point of latitude 59 degrees N, the north celestial pole is 59 degrees above the horizon (the observer is in the Northern hemisphere).
Therefore, the angular distance from the northern horizon up to the north celestial pole is 59 degrees. This means that, if you stand at a point of latitude 59 degrees N, you will observe the north celestial pole 59 degrees above the northern horizon. This phenomenon happens because the Earth rotates on its axis, which makes the stars appear to rotate around the celestial pole.
To know more about the celestial pole visit:
https://brainly.com/question/30418300
#SPJ11
How much work can a 1000-watt motor do in 5.0 seconds?
A. 4.0 × 101 J
B. 2.0 × 102 J
C. 5.0 × 103 J
D. 2.5 × 104 J
Answers
Explanation:
\(power = \frac{work}{time} \)
Given
POWER=1000 W
TIME=5s
WORK=POWER×TIME
=1000×5
5×10³
OPTION C
A heat engine does 23 kJ of work during 1800 s. Find the power supplied by the engine.
Answers
Given,
The work done by the engine, W=23 kJ
The time it takes for the engine to do the given amount of the work, t=1800 s
The power is the time rate of change of transfer of energy or the energy transferred in unit time. Thus the power supplied by the engine can be calculated as the ratio of the work done to the time.
Thus the power supplied by the engine is given by,
\(P=\frac{W}{t}\)On substituting the known values,
\(\begin{gathered} P=\frac{23\times10^3}{1800} \\ =12.78\text{ W} \end{gathered}\)Thus the power supplied by the engine is 12.78 W.
When the south poles of two bar magnets are brought close together,
there will be: *
a) a force of attraction.
b) a force of repulsion.
c) an upward force.
d) no forces
Answers
there will be
a)Aforce of attraction
what is the measure of apb if the measure of arc ab is 130
Answers
If the measure of arc AB is 130 degrees, the measure of angle APB is half of that since the angle subtended by an arc at the center of a circle is twice the angle subtended at any point on the circumference. Therefore, the measure of angle APB would be 65 degrees.
When dealing with a circle, the measure of an angle formed by two intersecting lines is related to the measure of the arc intercepted by those lines. In this case, the measure of arc AB is given as 130 degrees.
According to the inscribed angle theorem, an inscribed angle is equal to half the measure of its intercepted arc. Therefore, the angle APB, formed by lines AP and BP, will have a measure equal to half of the measure of arc AB.
Since arc AB measures 130 degrees, we can calculate the measure of angle APB by dividing 130 by 2, resulting in 65 degrees. Thus, the measure of angle APB is 65 degrees.
This relationship between arcs and angles is based on the properties and geometry of circles. By understanding these principles, we can determine the measures of angles based on given arc measures and vice versa.
To know more about geometry, visit:
https://brainly.com/question/31408211
#SPJ11
100 POINTS
Plutonium-235
Given: energy released = about 200 MeV per individual reaction (mass = 239 amu)
Part A
List the balanced nuclear reaction.
I NEED THIS ASAP
Answers
Answer:
One gram atom of any substance contains one Avogadro number of atoms. Therefore, the number of atoms of U-235 present in 235 g of the substance = Avogadro Number = 6.02×10^23 atoms
The number of U-235 atoms present in 1 g of the substance = (6.02×10^23/235) atoms=2.56×10^21 atoms
Energy released in one atom fissioning = 200 MeV= 200 MeV × 1.6 × 10^-6 erg/MeV= 3.2 ×10^-4 erg/atom.
Energy released in the fission of all the atoms contained in 1g of Uranium-235 fissioning = (2.56×10^21 atom)×(3.2×10^-4 erg/atom)=8.19 ×10^17 erg
Now
1 kWh = 1000 Watt hour = 1000×( 10^7 erg/s)×3600s = 3.6 ×10^13 erg/kWh
So energy in kWh released in fission of 1 g of U-235 = (8.19× 10^17 erg)÷(3.6×10^13 erg/kWh) = 2.55 ×10⁴ kWh.
Added on 19th February, 2019.
The energy consumption of an average home in India in a month is between 300–500 kWh in the metropolitan cities. Let us take it at 400 kWh. So one gram of nuclear fuel (uranium) would be able to meet the energy requirements of a town of about 6000 for a month.
The energy in a fissile material is highly concentrated, compared to other types of fuels like wood, coal, diesel etc. So nuclear powered submarines can remain below water for very long periods of time, as they do not need to surface for getting fuel.
Explanation:
Energy in kWh released in fission of 1 g of U-235 is 2.55 ×10⁴ kWh.
How do find the energy released in fission?One gram atom of any substance contains one Avogadro number of atoms. Therefore, the number of atoms of U-235 present in 235 g of the substance = Avogadro Number = 6.02×10^23 atoms
The number of U-235 atoms present in 1 g of the substance = (6.02×10^23/235) atoms=2.56×10^21 atoms
Energy released in one atom fissioning = 200 MeV= 200 MeV × 1.6 × \(10^{-6}\) erg/MeV= 3.2 ×\(10^{-4}\) erg/atom.
The energy released in the fission of all the atoms contained in 1g of Uranium-235 fissioning = (2.56×\(10^{21}\) atom)×(3.2×\(10^{-4}\) erg/atom) = 8.19 ×\(10^{17}\) erg
1000 Watt hour = 1000×( \(10^{7}\) erg/s)×3600s = 3.6 ×10^13 erg/kWh
So the energy in kWh released in fission of 1 g of U-235 = 2.55 ×10⁴ kWh.
Fission takes place when a neutron slams into a bigger atom, forcing it to excite and break up into smaller atoms—additionally referred to as fission products. Extra neutrons are also launched that may initiate a sequence reaction. whilst each atom splits, a high-quality amount of electricity is released.
Learn more about Fission here: brainly.com/question/4675347
#SPJ2
What is the reason for a stone sink in the water but a plastic floats?
Select one:
A.
The density of plastic is greater than stone
B.
Mass of the stone is greater than mass of plastics.
C.
The density of plastic is greater than water.
D.
The density of stone is greater than water.
Answers
If something is more dense than water it sinks but if it’s less dense it floats. The plastic floats because the plastic is less dense than the water but the stone sinks because it is more dense
Describe an activity to demonstrate magnetic induction.
Answers
In terms of net charge, how does an electrically polarized object differ from an electrically charged object?.
Answers
Answer:
An electrically polarized object can have zero net charge, while a charged object cannot have zero net charge.
I hope this helps :D
How do I find the average power of resistors with AC and DC voltage sources?
Answers
To find the average power of resistors with AC and DC voltage sources, you first need to calculate the power dissipated by the resistor for each source.
For AC sources, you can use the formula P=V*I*cosφ, where V is the RMS voltage, I is the RMS current, and φ is the phase angle.
For DC sources, you can use the formula P=V*I, where V is the voltage and I is the current. Once you have the power dissipated for each source, you can find the average power of the resistors by taking the average of the two powers.
To know more about resistor refer to-
brainly.com/question/24297401#
#SPJ11
If the voltage of a circuit is doubled and the resistance remains unchanged, the current flowing through the circuit will be
Answers
If the voltage of a circuit is doubled and the resistance remains unchanged, then current flowing through the circuit: will Increase
Relationship between Current, Voltage and Resistance
The Current of a circuit is directly proportional to the voltage and inversely proportional to the resistance.
The voltage in a circuit is equal to the product of the current and the resistance in the circuit
The resistance in a circuit is directly proportional to the voltage but inversely proportional to the current.
In conclusion, If the voltage of a circuit is doubled and the resistance remains unchanged, then current flowing through the circuit: will Increase
Learn more about current: https://brainly.com/question/24858512
#SPJ1
Question in the photo
Answers
Answer:
a lever that is what is used
The working formula for the electric charge (eq. (13) in the text) contains a constant involving the properties of the gas environment, the plastic sphere, and the electric field chamber combined in eq. -12. List these properties, together with their si units of measurement?
Answers
The working formula for the electric charge is given by:
q = CεE
where q is the electric charge, C is the constant involving the properties of the gas environment, the plastic sphere, and the electric field chamber, ε is the permittivity of the gas environment, and E is the electric field strength.
The properties involved in the constant C are:
1. The radius of the plastic sphere (r) - measured in meters (m)
2. The pressure of the gas environment (P) - measured in Pascals (Pa)
3. The temperature of the gas environment (T) - measured in Kelvin (K)
4. The number density of the gas environment (n) - measured in number of particles per cubic meter (m-3)
5. The mobility of the ions in the gas environment (μ) - measured in meters squared per Volt-second (m2V-1s-1)
These properties are combined in the constant C to give the electric charge of the plastic sphere in the electric field chamber.
More such questions on the working formula for the electric charge can be gotten here: https://brainly.com/question/30575187
#SPJ11
what pressure gradient along a streamline, dp/ds, will accelerate water (a) down a vertical pipe at 6 m/s2? (b) up a vertical pipe at 16 m/s2? give magnitude and sign.
Answers
The pressure gradient along a streamline required to accelerate water down a vertical pipe at 6 m/s² is -6000 Pa/m. The pressure gradient required to accelerate water up a vertical pipe at 16 m/s² is +16000 Pa/m.
In fluid dynamics, the pressure gradient along a streamline is responsible for the acceleration of the fluid. It represents the change in pressure per unit distance along the streamline. The sign of the pressure gradient indicates the direction of the acceleration. A negative pressure gradient indicates a decrease in pressure in the direction of flow, while a positive pressure gradient indicates an increase in pressure in the direction of flow.
For water to accelerate downward at 6 m/s², a negative pressure gradient of -6000 Pa/m is required. This means that the pressure decreases by 6000 Pa for every meter of distance along the streamline in the downward direction.
Conversely, for water to accelerate upward at 16 m/s², a positive pressure gradient of +16000 Pa/m is required. This means that the pressure increases by 16000 Pa for every meter of distance along the streamline in the upward direction.
By controlling the pressure gradient, the acceleration of water in a specific direction can be achieved.
Learn more about pressure gradient here
https://brainly.com/question/31975659
#SPJ11