![Give the result of operating on the function Ψ( y ) = e( [(-4 rV2] ) with the operator [ ^(A)] = [(d)/(dy)] Submit Answer Tries o/3 is the function Ψ( y )に [(-4y2)/2] ) an eigenfunction of the operator [(A)] [(d)/(dy)]? (yes, no) Submit Answer Tries 0/3](http://img.homeworklib.com/questions/f34ce800-733b-11ea-a17b-312030e02d56.png?x-oss-process=image/resize,w_560)
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Give the result of operating on the function Ψ( y ) = e( [(-4 rV2] )...
Give the result of operating on the function ЧС y ) g( [(-4 y )/2] )...
Give the result of operating on the function ЧС y ) g( [(-4 y )/2] ) with the operator [^(A)] -[(d2)/(dy2)]+16 y2 Submit Answer Tries 0/3 Is the function wC y )-e( [(-4 r2)/2) an eigenfunction of the operator [(A)]- -[(d2)/(dy2)]+16 y2? ("yes", "no") Submit Answer Tries 0/3 What is the eigenvalue of [^(A)] -[(d2)/(dy2)1+16 y2 operating on џ( y )-e( 1-4) /21) Submit Answer Tries 0/3
What would be the result of a kinetic energy measurement on a free quantum particle? (i.e....
What would be the result of a kinetic energy measurement on a free quantum particle? (i.e. potential energy V(x) = 0) of mass m with a wave-function ψ(x) = e^(-x^2) A hint for this question: Consider only the kinetic energy operator. Is the given function an eigenfunction of this operator? If yes, what will be the result of the measurement? If not an eigenfunction, what would be the result of the measurement?
Consider the function y(φ)-e",-ie h2 d where I is a constant? If so, what is the a) Is it an eige...
Consider the function y(φ)-e",-ie h2 d where I is a constant? If so, what is the a) Is it an eigenfunctions of the operator O-- eigenvalue? (answer: no) b) Normalize the function on the domain 0 φś2π (in this case, normalization implies | | ψ(0) 12 dφ= 1 ). Euler's identity, etimp-cos(mo) ± isin(mo), where m is a constant, will be useful (φ)-F(e"-ie")) to evaluate the normalization constant. (answer: ya normalized
Consider the function y(φ)-e",-ie h2 d where I is...
Let the joint probability density function for (X, Y) be f(x,y) s+y), x>0, y>0, 7r+yCT, 0...
Let the joint probability density function for (X, Y) be f(x,y) s+y), x>0, y>0, 7r+yCT, 0 otherwise. a. Find the probability P(X< Y). Give your answer to 4 decimal places. 28 Submit Answer Tries 0/5 b. Find the marginal probability density function of X, fx(x). Enter a formula in the first box, and a number for the second and the third box corresponding to the range of x. Use * for multiplication, / for division and л for power. For...
3. Consider the wave function ψ(x)- 슬 읔 ets, where σ s a real valued constant...
3. Consider the wave function ψ(x)- 슬 읔 ets, where σ s a real valued constant (a) Calculate the expectation value of K). K (b) Estimate the uncertainty Δ.r and Ap using Δ.1-V (.12)-(A)2. 4. Consider the eigenfunctions of the moment uni operator y p r her (a) Show that p,(r) is an eigenfunction of p with an cigenvalue p. (b) Find the coeflicients. w, in the espansion of (r)( upypp ) using the momentum eigenfunctions.
1. Show y = sin ax is not an eigenfunction of the operator d/dx, but is...
1. Show y = sin ax is not an eigenfunction of the operator d/dx, but is an eigenfunction of the operator da/dx. 2. Show that the function 0 = Aeimo , where i, m, and A are constants, is an eigenfunction of the angular momentum operator is the z-direction: M =; 2i ap' and what are the eigenvalues? 3. Show the the function y = Jź sin MA where n and L are constants, is an eigenfunction of the Hamiltonian...
Q3) A particle in the harmonic oscillator potential has the initial normalized wave function Ψ(?, 0)...
Q3) A particle in the harmonic oscillator potential has the initial normalized wave function Ψ(?, 0) = 1 /√5 [2 ?₁ (?) + ?₂ (?)] where ?1 and ?2 are the eigenfunctions of the oscillator Hamiltonian for ? = 1,2 states. a) Write down the expression for Ψ(?,?). b) Calculate the probability density ℙ(?,?) = |Ψ(?,?)| ² . Express it as a sinusoidal function of time. To simplify the result, let ? ≡ (?² ℏ)/ 2??² . c) Calculate 〈?〉...
Thank you! Q8 Consider two independent continuous random variables X and Y with probability density function...
Thank you!
Q8 Consider two independent continuous random variables X and Y with probability density function given as follows: fx(x) 1/10, 0<x< 10 0 otherwise 0y 10 fro-6/10, (y) = Enter all answers as a fraction (e.g. 4/5) or integer. a. Create the joint pdf from the marginals: <<y<0 otherwise. Submit Answer Tries 0/15 b, Find E(X 1 Y 2) Submit Answer Tries 0/5 C. Find E(Y 1 X = 2) Submit Answer Tries 0/5 d. Find Cov(X, Y) Submit...
Problems binomial random variable has the moment generating function ψ(t)-E( ur,+1-P)". Show, that EIX) np and...
Problems binomial random variable has the moment generating function ψ(t)-E( ur,+1-P)". Show, that EIX) np and Var(X)-np(1-P) using that EXI-v(0) and Elr_ 2. Lex X be uniformly distributed over (a b). Show that EX]- and Varm-ftT using the first and second moments of this random variable where the pdf of X is () Note that the nth i of a continuous random variable is defined as E (X%二z"f(z)dz. (z-p?expl- ]dr. ơ, Hint./ udv-w-frdu and r.e-//agu-VE. 3. Show that 4 The...
Let X be a random variable with probability density function fx(2, -1 9. f(y) y> 9. Submit Answe...
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Let X be a random variable with probability density function fx(2, -1 <z<3, 0 otherwise. Find the probability distribution of Y-X2 for 0 < y < 1, 1 < y < 9, and y > 9. [Obviously, fy(y)-0 for y < 0.1 Case 1: O < y < 1. Enter a formula below. Use * for multiplication, / for divison, ^ for power and sqrt for square root. For example, sqrt y...
Give the result of operating on the function ЧС y ) g( [(-4 y )/2] ) with the operator [^(A)] -[(d2)/(dy2)]+16 y2 Submit Answer Tries 0/3 Is the function wC y )-e( [(-4 r2)/2) an eigenfunction of the operator [(A)]- -[(d2)/(dy2)]+16 y2? ("yes", "no") Submit Answer Tries 0/3 What is the eigenvalue of [^(A)] -[(d2)/(dy2)1+16 y2 operating on џ( y )-e( 1-4) /21) Submit Answer Tries 0/3
Consider the function y(φ)-e",-ie h2 d where I is a constant? If so, what is the a) Is it an eigenfunctions of the operator O-- eigenvalue? (answer: no) b) Normalize the function on the domain 0 φś2π (in this case, normalization implies | | ψ(0) 12 dφ= 1 ). Euler's identity, etimp-cos(mo) ± isin(mo), where m is a constant, will be useful (φ)-F(e"-ie")) to evaluate the normalization constant. (answer: ya normalized
Consider the function y(φ)-e",-ie h2 d where I is...
Let the joint probability density function for (X, Y) be f(x,y) s+y), x>0, y>0, 7r+yCT, 0 otherwise. a. Find the probability P(X< Y). Give your answer to 4 decimal places. 28 Submit Answer Tries 0/5 b. Find the marginal probability density function of X, fx(x). Enter a formula in the first box, and a number for the second and the third box corresponding to the range of x. Use * for multiplication, / for division and л for power. For...
3. Consider the wave function ψ(x)- 슬 읔 ets, where σ s a real valued constant (a) Calculate the expectation value of K). K (b) Estimate the uncertainty Δ.r and Ap using Δ.1-V (.12)-(A)2. 4. Consider the eigenfunctions of the moment uni operator y p r her (a) Show that p,(r) is an eigenfunction of p with an cigenvalue p. (b) Find the coeflicients. w, in the espansion of (r)( upypp ) using the momentum eigenfunctions.
1. Show y = sin ax is not an eigenfunction of the operator d/dx, but is an eigenfunction of the operator da/dx. 2. Show that the function 0 = Aeimo , where i, m, and A are constants, is an eigenfunction of the angular momentum operator is the z-direction: M =; 2i ap' and what are the eigenvalues? 3. Show the the function y = Jź sin MA where n and L are constants, is an eigenfunction of the Hamiltonian...
Thank you!
Q8 Consider two independent continuous random variables X and Y with probability density function given as follows: fx(x) 1/10, 0<x< 10 0 otherwise 0y 10 fro-6/10, (y) = Enter all answers as a fraction (e.g. 4/5) or integer. a. Create the joint pdf from the marginals: <<y<0 otherwise. Submit Answer Tries 0/15 b, Find E(X 1 Y 2) Submit Answer Tries 0/5 C. Find E(Y 1 X = 2) Submit Answer Tries 0/5 d. Find Cov(X, Y) Submit...
Problems binomial random variable has the moment generating function ψ(t)-E( ur,+1-P)". Show, that EIX) np and Var(X)-np(1-P) using that EXI-v(0) and Elr_ 2. Lex X be uniformly distributed over (a b). Show that EX]- and Varm-ftT using the first and second moments of this random variable where the pdf of X is () Note that the nth i of a continuous random variable is defined as E (X%二z"f(z)dz. (z-p?expl- ]dr. ơ, Hint./ udv-w-frdu and r.e-//agu-VE. 3. Show that 4 The...
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Let X be a random variable with probability density function fx(2, -1 <z<3, 0 otherwise. Find the probability distribution of Y-X2 for 0 < y < 1, 1 < y < 9, and y > 9. [Obviously, fy(y)-0 for y < 0.1 Case 1: O < y < 1. Enter a formula below. Use * for multiplication, / for divison, ^ for power and sqrt for square root. For example, sqrt y...
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