1. Show that [x",p] = ihnx"-1 [10]
Answers
Here is a way to show that [x",p] = ihnx"-1 [10].
To prove the commutation relation [x", p] = iħnx"-1, where x" and p are the position and momentum operators, respectively, we can use the ladder operator method.
First, let's define the position and momentum operators in terms of the ladder operators a and a†:
x" = (√(ħ/2mw))(a† + a)
p = i(√(mħw/2))(a† - a)
where m is the mass of the particle and w is the angular frequency.
Now, let's substitute these expressions into the commutation relation:
[x", p] = [(√(ħ/2mw))(a† + a), i(√(mħw/2))(a† - a)]
Expanding the expression, we get:
[x", p] = (√(ħ/2mw))(a† + a)(i(√(mħw/2))(a† - a)) - i(√(mħw/2))(a† - a)(√(ħ/2mw))(a† + a)
Simplifying, we have:
[x", p] = (√(ħ/2mw))(iħ(a†a† - a†a) + a†a - aa†) - (√(ħ/2mw))(iħ(a†a† - a†a) - a†a + aa†)
Using the commutation relation [a, a†] = 1, we can rearrange the terms:
[x", p] = (√(ħ/2mw))(iħ(a†a† - a†a + a†a - aa†))
Further simplifying, we get:
[x", p] = (√(ħ/2mw))(iħ(a†a† - aa†))
Now, let's express the operator a†a† and aa† in terms of the number operator n = a†a:
a†a† = (n + 1)a†
aa† = na
Substituting these expressions back into the commutation relation, we have:
[x", p] = (√(ħ/2mw))(iħ((n + 1)a† - na))
Expanding, we get:
[x", p] = (√(ħ/2mw))(iħna† - iħna + iħa†)
Simplifying, we have:
[x", p] = (√(ħ/2mw))(iħa† - iħa)
Finally, we can rewrite the expression using the relation [a†, a] = -1:
[x", p] = iħna† - iħna = iħn(a† - a) = iħnx"-1
Therefore, we have shown that [x", p] = iħnx"-1, as required.
To know more about commutation relation refer here:
https://brainly.com/question/570254?#
#SPJ11
Related Questions
describe y as the sum of two orthogonal vectors, x1 in span{u} and x2 orthogonal to u.
Answers
To describe y as the sum of two orthogonal vectors, x1 in the span{u} and x2 orthogonal to u , we follow two steps procedure:
1.First, find a vector x1 in the span{u} that is the projection of y onto u. To do this, use the formula:
x1 = (y • u / ||u||^2) * u, where • represents the dot product and || || represents the magnitude of the vector.
2.Next, find the vector x2 that is orthogonal to u. Since y can be represented as the sum of x1 and x2, you can find x2 by subtracting x1 from y:
x2 = y - x1
3.Now, you have y as the sum of two orthogonal vectors x1 and x2, with x1 in the span{u} and x2 orthogonal to u.
Learn more about at orthogonal vectors brainly.com/question/29423004
#SPJ11
Given A= [ -2 3 3 -3] and B= [1 2 -1 2] use the Frobenius inner product and the corresponding induced norm to determine the value of each of the following: (A,B) =
||A||f =
||B|| =
0 A.B =
Answers
The value of (A, B) is -5 and the Frobenius norms of A and B are √31 and √10, respectively.
The value of each of the following expressions can be determined using the Frobenius inner product and the corresponding induced norm:
(A, B): The Frobenius inner product of two matrices A and B is calculated by taking the element-wise product of the matrices and summing up all the elements. In this case, (A, B) = \(-21 + 32 + 3(-1) + (-3)2 = -2 + 6 - 3 - 6 = -5.\)
||A||f: The Frobenius norm of a matrix A is calculated by taking the square root of the sum of the squares of all the elements in the matrix. In this case, ||A||f = √\(((-2)^2 + 3^2 + 3^2 + (-3)^2)\)= √(4 + 9 + 9 + 9) = √31.
||B||: Similarly, the Frobenius norm of matrix B is calculated as ||B|| = √(1^2 + \(2^2 + (-1)^2 + 2^2)\) = √(1 + 4 + 1 + 4) = √10.
A·B: The dot product of two matrices A and B is calculated by taking the element-wise product of the matrices and summing up all the elements. In this case, A·B = -21 + 32 + 3(-1) + (-3)2 = -2 + 6 - 3 - 6 = -5.
Therefore, (A, B) = -5, ||A||f = √31, ||B|| = √10, and A·B = -5.
Learn more about matrices here:
https://brainly.com/question/30646566
#SPJ11
What is the slope of the following line?
A. 1/3
B. - 1/3
C. 3
D. - 3
Answers
Answer:
A
Step-by-step explanation:
Points of origin are (-3,0) and (0,1). Now we determine if it is a positive slope, it is as it goes up not down. It goes up 1 unit and over to the right 3 units, making the slope 1/3.
Solve the equation AB=BC for A, assuming that A,B and C are square matrices and B is invertible.
Answers
The solution of AB = BC for A, assuming that A,B and C are square matrices and B is invertible is \(A = BCB^{-1}\)
We have to solve the equation
AB = BC , given that these all are square matrices and B is invertible.
Write the required Equation:
AB = BC
Multiply both sides by inverse of B
The multiplicative inverse of a matrix is the matrix that gives you the identity matrix when multiplied by the original matrix.
Matrix multiplied by an identity matrix, the result is always the same original non-identity (non-unit) matrix, and thus, as explained before, the identity matrix gets the nickname of "unit matrix"
\(ABB^{-1} = BCB^{-1}\\AI = BCB^{-1}\\A = BCB^{-1}\)
so the solution of AB = BC is \(A = BCB^{-1}\)
To know more about matrix
https://brainly.com/question/13260356
#SPJ4
A CBS News/New York Times opinion poll asked 1,190 adults whether they would prefer balancing the federal budget over cutting taxes; 59% of those asked said "yes." Suppose that in fact 62% of all adults favor balancing the budget over cutting taxes. If this poll was not biased, what is the probability you would get p^=0.59 or less?
Answers
Using the normal distribution and the central limit theorem, it is found that there is a 0.0166 = 1.66% probability of a sample proportion of 0.59 or less.
In a normal distribution with mean \(\mu\) and standard deviation \(\sigma\), the z-score of a measure X is given by:
\(Z = \frac{X - \mu}{\sigma}\)
It measures how many standard deviations the measure is from the mean. After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X. By the Central Limit Theorem, the sampling distribution of sampling proportions of a proportion p in a sample of size n has mean \(\mu = p\) and standard error \(s = \sqrt{\frac{p(1 - p)}{n}}\)In this problem:
1,190 adults were asked, hence \(n = 1190\)In fact 62% of all adults favor balancing the budget over cutting taxes, hence \(p = 0.62\).The mean and the standard error are given by:
\(\mu = p = 0.62\)
\(s = \sqrt{\frac{p(1 - p)}{n}} = \sqrt{\frac{0.62(0.38)}{1190}} = 0.0141\)
The probability of a sample proportion of 0.59 or less is the p-value of Z when X = 0.59, hence:
\(Z = \frac{X - \mu}{\sigma}\)
By the Central Limit Theorem
\(Z = \frac{X - \mu}{s}\)
\(Z = \frac{0.59 - 0.62}{0.0141}\)
\(Z = -2.13\)
\(Z = -2.13\) has a p-value of 0.0166.
0.0166 = 1.66% probability of a sample proportion of 0.59 or less.
You can learn more about the normal distribution and the central limit theorem at https://brainly.com/question/24663213
Who’s willing to help? :)
Answers
Answer:
1- 77
2- 39
3- 50
4- 46
5- 49
6- 67
7- 29
8- 9
9- 15
10- 22
Step-by-step explanation:
P) Parentheses
E) Exponents
M) Multiplication
D) Division
A) Addition
S) Subtraction
Left to right
A sphere has a volume that is 36 cubic meters. Find the radius of the sphere.
Answers
Answer:
2.05m
Step-by-step explanation:
Is the following equation Linear, Non-linear, or neither
5x +2(x3 - 9) = 132 + 8x?
Answers
Answer:
x = 50
Step-by-step explanation:
5x + 2(3x - 9) = 132 + 8x
5x + 6x - 18 = 132 + 8x
11x - 18 = 132 + 8x
11x - 18 = 8x + 132
11x - 18 + 18 = 8x + 132 + 18
11x = 8x + 150
11x - 8x = 8x - 8x + 150
3x = 150
3x ÷ 3 = 150 ÷ 3
x = 50
cherie left at 7:10 to drive to her aunts house her aunts lives 339 miles away she arrived at 12:55 how long did it take cherie to drive to her aunt house
Answers
Answer:
17hrs 45mins
Step-by-step explanation:
Timespan is 17 hour(s) and 45 minute(s).
Suppose that a certain property is located in a state that uses the government rectangular survey system for legal descriptions of property. If the property is located 57 miles north and 38 miles west of the starting point for property descriptions which township is it located in
Answers
The property descriptions which the township is located in is 9 North and Range 6 West
How to determine the townshipThe townships serve as the main elements in the government's rectangular survey approach for identifying the position of properties. A township comprises a square region of six miles on all its four sides.
In order to ascertain the exact township where the property is situated, it is necessary to compute the township coordinates using the specified distance.
From the information given, we have to convert the distance to township units.
We have;
57 miles north / 6 miles = 9.5 townships north
38 miles west / 6 miles = 6.33 townships west
Learn more about government survey system at: https://brainly.com/question/31755405
#SPJ4
a pole that is 2.8m tall casts a shadow that is 1.49m long. at the same time, a nearby building casts a shadow that is 37.5m long. how tall is the building? round your answer to the nearest meter.
Answers
The height of the building is 71 meters.
We can solve this problem using the similar triangles. The height of the building can be determined by setting up the following proportion:
(the height of pole) / (length of pole's shadow) = (height of building) / (length of building's shadow)
Substituting the given values:
2.8 / 1.49 = (height of building) / 37.5
To find the height of the building, we can cross-multiply and solve for it:
(2.8 * 37.5) / 1.49 = height of building
Calculating the expression on the right side:
(2.8 * 37.5) / 1.49 ≈ 70.7013
Rounding to the nearest meter, the height of the building is approximately 71 meters.
Learn more about heigth building at https://brainly.com/question/7289008
#SPJ11
Consider a plate with a radial density of rho(x)=7x+4 and radius 1. What is the mass of the plate?
Answers
The mass of the plate (22/3)π.
The problem says that the radial density function is equal to two times the average density of the plate, and that the radius is the same.
The mass of the plate can be found by integrating the radial density over the area of the plate.
Using the formula for the area of a circle, A = πr², we can find the mass as follows:
M = ∫₀¹ρ(x) dA
= ∫₀¹(7x+4) dA
= ∫₀¹(7x+4) (2πx) dx
= 2π ∫₀¹(7x²+4x) dx
= 2π [(7/3)x³ + 2x²]₀¹
= 2π [(7/3)(1)³ + 2(1)² - (7/3)(0)³ - 2(0)²]
= 2π [(7/3) + 2]
= 2π (11/3)
= (22/3)π
Therefore, the mass of the plate is (22/3)π.
Know more about mass here:
https://brainly.com/question/19385703
#SPJ11
find the value 1/2+1/3+1/4=
plz answer step by step
i will give you 5 star
Answers
Answer:
\(\frac{13}{12}\)
Step-by-step explanation:
Find the LCM of 2, 3, 4: 12Alter the numerators to fit the denominators (steps not shown): \(\frac{6}{12} + \frac{4}{12} + \frac{3}{12}\) \(\frac{6}{12} + \frac{4}{12} + \frac{3}{12} = \frac{13}{12}\)I hope this helps!
The following data are taken from a study conducted by the National Park Service, of which Death Valley is a unit. The ground temperature (oF) were taken from May to November in the vicinity of Furnace Creek. Compute the interquartile range.
Answers
To compute the interquartile range (IQR), we need the dataset containing the ground temperatures taken from May to November in the vicinity of Furnace Creek.
Without the actual dataset, I won't be able to provide you with the exact IQR. However, I can explain the process of calculating the interquartile range once you have the dataset.
The interquartile range is a measure of statistical dispersion and represents the range between the first quartile (Q1) and the third quartile (Q3). Here's how you can calculate it:
1. Arrange the dataset in ascending order.
2. Find the median of the dataset, which is the value separating the lower half from the upper half.
3. Split the dataset into two halves: the lower half (values less than or equal to the median) and the upper half (values greater than or equal to the median).
4. Find the median of the lower half, which becomes Q1.
5. Find the median of the upper half, which becomes Q3.
6. Calculate the interquartile range (IQR) by subtracting Q1 from Q3: IQR = Q3 - Q1.
Once you provide the dataset, I can help you calculate the interquartile range using the steps outlined above.
Learn more about Interquartile Range here:
https://brainly.com/question/4135956
#SPJ11
Based on this data, what is a reasonable estimate of the probability that Patsy sells fewer than 5 feathers next festival?
Answers
A reasonable estimate of the probability that Patsy sells fewer than 2 feathers at the next festival is about 0.2485.
How to estimate the probability of given data?
To estimate the probability that Patsy sells fewer than a certain number of feathers at the next festival, we need to use the given data to calculate the mean and standard deviation of the number of feathers she has sold in the past festivals.
The mean, denoted by μ, is calculated by adding up all the number of feathers sold and dividing by the total number of festivals. So,
μ = (3 + 6 + 1 + 4 + 2 + 3 + 7 + 2) / 8 = 3.375
The standard deviation, denoted by σ, is a measure of how spread out the data is. It is calculated by first finding the variance, which is the average of the squared differences between each data point and the mean, and then taking the square root of the variance. So,
Variance = ((3-3.375)² + (6-3.375)²+ (1-3.375)² + (4-3.375)² + (2-3.375)² + (3-3.375)² + (7-3.375)² + (2-3.375)²) / 8 = 4.0898
σ = √(4.0898) = 2.022
Now, to estimate the probability that Patsy sells fewer than a certain number of feathers at the next festival, we need to standardize the value by subtracting the mean and dividing by the standard deviation. So, let X be the number of feathers sold at the next festival, then,
Z = (X - μ) / σ
Let's say we want to estimate the probability that Patsy sells fewer than 2 feathers at the next festival. Then,
Z = (2 - 3.375) / 2.022 = -0.679
We can use a standard normal distribution table or calculator to find the probability that a standard normal random variable is less than -0.679, which is approximately 0.2485.
Therefore, a reasonable estimate of the probability that Patsy sells fewer than 2 feathers at the next festival is about 0.2485.
Learn more about estimate here,
https://brainly.com/question/29436481
#SPJ1
Correct question is "The number of feathers Patsy 3, 6, 1, 4, 2, 3, 7, 2 Peacock sold at each of the festivals this year. Based on this data, what is a reasonable estimate of the probability that Patsy sells fewer than feathers next festival? "
At appliance store, 37% of customers purchase a wahing machine. 11 % of customers buy both a wahsing machine. 11% of customers buy both waher and a dryer. Find the probability that a customer who buys a washer also buys a dryer
Answers
The probability that a customer who buys a washer also buys a dryer is 0.297 or approximately 30%.
To find the probability that a customer who buys a washer also buys a dryer, we need to use conditional probability.
Let's start by finding the probability of a customer buying a washer and a dryer, which is given as 11%.
Now, we know that 11% of customers buy both a washer and a dryer. We also know that 37% of customers buy a washer.
Using these two pieces of information, we can find the probability of a customer buying a dryer given that they have already bought a washer. This is the conditional probability we are looking for.
The formula for conditional probability is:
P(D | W) = P(D and W) / P(W)
where P(D | W) is the probability of buying a dryer given that a washer has already been purchased, P(D and W) is the probability of buying both a dryer and a washer, and P(W) is the probability of buying a washer.
Substituting the values we have:
P(D | W) = 0.11 / 0.37
P(D | W) = 0.297
The probability that a customer who buys a washer also buys a dryer is 0.297 or approximately 30%.
Learn more about probability,
https://brainly.com/question/24756209
#SPJ11
Question 38.
Write the first six terms of the arithmetic sequence with the first term, a1 = 240, and common difference, d= 24.
The first six terms are a1 = ,a3= , a4= ,a5= , and a6= .
Answers
\(a(1) = 240 \\ a(2) = a(1) + d = 240 + 24 = 264 \\ a(3) = a(2) + d = 264 + 24 = 288 \\ a(4) = a(3) + d = 288 + 24 = 312 \\ a(5) = a(4) + d = 312 + 24 = 336 \\ a(6) = a(5) + d = 336 + 24 = 360\)
Answers to questions A and B
Answers
Answer:
A. m(arc BC) = 16°
B. m(arc BAC) = 344°
Step-by-step explanation:
From the picture attached,
AB is the diameter of the circle.
Since, measure of an arc is always same as the central angle of arc.
Therefore, m(arc AC) = m(∠ADC) = 164°
m(arc AB) = 180°
m(arc BC) = 360° - m(arc AB) + m(arc AC)
= 360° - (180° + 164°)
= 360° - 344°
= 16°
m(arc BAC) = m(arc AB) + m(arc AC)
= 180° + 164°
= 344°
mr. dyer pours 2 cups of blue paint into a jar for each art station. how many jars can he fill with 1 gallon of blue paint?
Answers
If Mr. Dyer pours 2 cups of blue paint into a jar for each art station, then the he can fill 8 jars with 1 gallon of blue paint.
Number of cups of blue paint for each art station = 2 cups
Given that,
One cup = 8 ounce
1 gallon = 128 ounce
2 cups of blue paint = 2 × 8
= 16 ounce of blue paint
1 gallon of blue paint = 128 ounce of blue paint
Number of jars that he can fill with 1 gallon of blue paint = 1 gallon of blue paint / 2 cups of blue paint
Here we have to use division
= 128/16
= 8 jars
Hence, if Mr. Dyer pours 2 cups of blue paint into a jar for each art station, then the he can fill 8 jars with 1 gallon of blue paint.
The complete question is:
Mr. dyer pours 2 cups of blue paint into a jar for each art station. how many jars can he fill with 1 gallon of blue paint? One cup = 8 ounce and 1 gallon = 128 ounce
Learn more about division here
brainly.com/question/21416852
#SPJ4
The diameter of a circle is 9 ft. Find the circumference and round it to the nearest tenth.
Answers
Answer:
9*3.14=28.26
Step-by-step explanation:
Hope this Helps!
Answer:
\(C\approx28.27ft\)
Step-by-step explanation:
\(C=\pi d\\C=\pi(9)\\C=9\pi\\C\approx28.27\)
Thus, your circumference is about 28.27 ft
help meeeee please i do not understand this
Answers
Answer:
10.4 g/cm³
Step-by-step explanation:
Find the volume with formula, l x b x h
Then the formula gram / volume to find density.
Emily uses 2/3 cup of milk to make one batch of muffins .How many cups of milk will Emily use if she makes 3 batches of muffins?
Answers
Answer:2
Step-by-step explanation:
2/3 * 3 is 6/3 which is 2
Find the height of a cone with a diameter of 12 m whose volume is 226 m^3
Use 3. 14 for pi and round your answer to the nearest meter.
Answers
The volume of a cone is given by the formula:
volume = (1/3) * pi * r^2 * h
where r is the radius of the base of the cone (half of the diameter), and h is the height of the cone.
We can rearrange this formula to solve for the height:
h = (3 * volume) / (pi * r^2)
Substituting the given values and solving for h gives:
h = (3 * 226 m^3) / (3.14159 * (12 m / 2)^2)
h = (3 * 226 m^3) / (3.14159 * 6^2 m^2)
h = (3 * 226 m^3) / (3.14159 * 36 m^2)
h = (3 * 226 m^3) / 113.097 m^2
h = 6.49 m
So the height of the cone is approximately 6.49 m.
In arithmetic, what is volume?A 3D object's volume is the amount of actual space it occupies. It is a 2D shape's 3D equivalent of area. It is quantified in cubic units like cm3. By multiplying its length, height, and width, you may determine this.
To know more about volume visit:
https://brainly.com/question/13338592
#SPJ4
is a circle a symmetrical
Answers
Answer:
yes
Step-by-step explanation:
ny shape that has a line of symmetry is symmetrical shape.means the shape can be folded into two equal halves.
An investor invests $525 in stock. For each month following, the stock increased at a rate of $25 per
month
Identify the slope of the linear relationship. Explain what the slope represents in the context of the
problem
• identify the y-intercept of the linear relationship. Explain what the y-intercept represents in the
context of the problem.
Create a model/build the function/write the equation in slope-intercept form to represent the total
value of the stock, f (2), based on the number of months, I.
Answers
Answer: f(x) = mx+ b
slope = m = $25 / month
This means that for every month (x) that goes by, the total value of the stock (f(x)) will increase by $25.
y-intercept = b = $525
This is the amount of money in the account at time = 0. This will be equal to the original investment of $525.
f(x) = mx+ b = 25x + 525
Step-by-step explanation:
find the exact value of the expression, if possible.arcsin[sin(9π/4)]
Answers
The exact value of the expression arcsin[sin(9π/4)] is π/4 or 45°.
Step-by-step explanation:
We know that the range of the arcsine function is from -π/2 to π/2.
Now, let's evaluate sin(9π/4). Since one full rotation is equal to 2π radians, we can subtract 2π radians from 9π/4 until we get an angle between 0 and 2π.
9π/4 - 2π = π/4
So, sin(9π/4) is equal to sin(π/4).
Now, we know that sin(π/4) = 1/√2.
Therefore, we can evaluate the given expression as:
arcsin[sin(9π/4)] = arcsin[sin(π/4)]
= arcsin[1/√2]
The arcsine of 1/√2 is equal to π/4 or 45°, since the sine is positive in the first and second quadrants.
Hence, the exact value of the expression arcsin[sin(9π/4)] is π/4 or 45°.
To learn more about arcsine function visit:https://brainly.com/question/1658915
#SPJ11
if it is 2:00 what time would it be a half hour later
Answers
Answer:
2:30
Step-by-step explanation:
A half hour is 30 minutes.
Answer:
\(\huge\boxed{2:30}\)
Step-by-step explanation:
Half hour is 30 minutes.
So, Adding 30 minutes to 2:00 will be:
=> 2:30
Hope this helped!
~AnonymousHelper1807
Find the distance between the two points in simplest radical form.
(0, –4) and (-3,-1)
Answers
Answer:
3\(\sqrt{2}\)
Step-by-step explanation:
Calculate the distance d using the distance formula
d = \(\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }\)
with (x₁, y₁ ) = (0, - 4) and (x₂, y₂ ) = (- 3, - 1)
d = \(\sqrt{(-3-0)^2+(-1+4)^2}\)
= \(\sqrt{(-3)^2+3^2}\)
= \(\sqrt{9+9}\)
= \(\sqrt{18}\)
= \(\sqrt{9(2)}\)
= \(\sqrt{9}\) × \(\sqrt{2}\) = 3\(\sqrt{2}\)
Step-by-step explanation:
Hey there!
Given;
The points are;(0,-4) and (-3,-1).
Use formula for distance between the two points.
\(d = \sqrt{ {(x2 - x1)}^{2} + {(y2 - y1)}^{2} } \)
Put all values.
\(d = \sqrt{( { - 3 - 0)}^{2} + ( { - 1 + 4)}^{2} } \)
Simplify to get answer.
\(d = \sqrt{9 + 9} \)
\(d = \sqrt{18} \)
\(d = 3 \sqrt{2} \)
Therefore, the distance is 3√(2) units or 4.24 units.
Hope it helps...
Circumference of Circle
Geometry
Answers
Answer:
the equation for the circumerence of a circle is pi R squared
Step-by-step explanation:
here the radius is 28
So it would be pi 28squared
so i think it would be 784pi
How do you rewrite 6^6*6^-2*6^5 using each base only once