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9. Show that the function w= sin(x) (n and a are constants) is an eigenfunction of...
Show that the function (n and a are constants) is a eigenfunction of the Hamiltonian operator...
Show that the function (n and a are constants) is a eigenfunction of the Hamiltonian operator . What are the eigenvalues? and m should be considered constant factors. **SIDE NOTE: All the question marks should actually be upside down. I did not see the symbol for this! We were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this image
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...
(a) Show that (@) = sin e- is an eigenfunction of both Î, and Î", where...
(a) Show that (@) = sin e- is an eigenfunction of both Î, and Î", where = -1 1 a 1 22 sin + sin 020 sin0 and derive the corresponding eigenvalues. You may use the identity 1 a 1 sin sin 2 sin sin 0 80 sino 31 (sin 00 (5 marks) (6) Consider the function $(,0,4)= A - 1/200 sin 6e-ip, 20 where A is a constant and an is the Bohr radius. This is a hydrogen atom...
• Problem 7. For a wave-function W.(x) = (2/a)" sin(x/a) calculate the average position (<x>). Is...
• Problem 7. For a wave-function W.(x) = (2/a)" sin(x/a) calculate the average position (<x>). Is the function W.(x) = (2/a) sin(x/a) an eigenfunction of the x operator?
A function Ψ(x) is an eigenfunction of an operator A with an eigenvalue λ if Ay(x)-AW(x)...
A function Ψ(x) is an eigenfunction of an operator A with an eigenvalue λ if Ay(x)-AW(x) where λ is some number. Show that the function ψ(x)-xe-rn is an eigenfunction of the operator A--x2. What is the eigenvalue?
1. (50 points) Consider the particle in a one-dimensional box (0 s x S L). Assume a term is added to the Hamiltonian of the form: πχ V(x)g sin Sketch the potential and the expected eigenfunction (...
1. (50 points) Consider the particle in a one-dimensional box (0 s x S L). Assume a term is added to the Hamiltonian of the form: πχ V(x)g sin Sketch the potential and the expected eigenfunction (small g). In the limit of small g, find the second order correction to the ground state energy 2. (50 points) For a diatomic molecule rotating in free space, the Hamiltonian may be written: 12 21 Where L is the total angular momentum operator,...
Consider the finite difference matrix operator for the 1D model problem u(/d2- f(x) on domain [0,...
Consider the finite difference matrix operator for the 1D model problem u(/d2- f(x) on domain [0, 1] with boundary conditions u(0) = 0 and u(1) = 0, given by [-2 1 1-2 1 E RnXn h2 1 -2 1 This matrix can be considered a discrete version of the continuous operator d/da2 that acts upon a function(r). (a) Show that the n eigenvectors of A are given by the vectors ) (p-1,... , n) with components and with eigenvalues h2...
question 7 9 10 ), where n, a, and are constant, is an eigenfunction of p....
question 7 9 10
), where n, a, and are constant, is an eigenfunction of p. 7. (a) p. =- what is p. ? (b) sin( i ax what is the eigenvalue? (107) (9) = v ydt for a normalized wavefunction. Please find (1) for(a) v. - and (b) 42p. 4/2008 re s in sind. (hint : integrate over all space: sin Odrdodø (sin? xdx = [l-c952de, 5 xede = (203) 3 2 10. A particle of mass m is...
Please answer number 8 l Verizon LTE 9:53 PM 100%,--+ Close Physical Chemistry ll Spring...1 DOCX-149...
Please answer number 8
l Verizon LTE 9:53 PM 100%,--+ Close Physical Chemistry ll Spring...1 DOCX-149 KB (e) none of the above 7. A free particle is inside a one dimentional box from 0 to a/2, (a is a constant). If the particle is in the first excited states with eigenfunction, y Nsin (4px/a) (a) Determine the normalization constant. (b) Calculate the probability in between a/4 and a/2 8. What is the degree of the degeneracy if the three quantum...
1) (35 points) The wave function for a particle moving along x axis between the limits 0 and L is: (x)-C sin (nx xL) where n are 1, 2, 3, A) Determine the normalization constant C B) Why can'...
1) (35 points) The wave function for a particle moving along x axis between the limits 0 and L is: (x)-C sin (nx xL) where n are 1, 2, 3, A) Determine the normalization constant C B) Why can't n take the value of 0, briefly explain C) For n-3 determine the values of x (in terms of L) that correspond to a maximum or a minimum in the wave function D) For n-3 determine the values of x (in...
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...
(a) Show that (@) = sin e- is an eigenfunction of both Î, and Î", where = -1 1 a 1 22 sin + sin 020 sin0 and derive the corresponding eigenvalues. You may use the identity 1 a 1 sin sin 2 sin sin 0 80 sino 31 (sin 00 (5 marks) (6) Consider the function $(,0,4)= A - 1/200 sin 6e-ip, 20 where A is a constant and an is the Bohr radius. This is a hydrogen atom...
• Problem 7. For a wave-function W.(x) = (2/a)" sin(x/a) calculate the average position (<x>). Is the function W.(x) = (2/a) sin(x/a) an eigenfunction of the x operator?
A function Ψ(x) is an eigenfunction of an operator A with an eigenvalue λ if Ay(x)-AW(x) where λ is some number. Show that the function ψ(x)-xe-rn is an eigenfunction of the operator A--x2. What is the eigenvalue?
1. (50 points) Consider the particle in a one-dimensional box (0 s x S L). Assume a term is added to the Hamiltonian of the form: πχ V(x)g sin Sketch the potential and the expected eigenfunction (small g). In the limit of small g, find the second order correction to the ground state energy 2. (50 points) For a diatomic molecule rotating in free space, the Hamiltonian may be written: 12 21 Where L is the total angular momentum operator,...
Consider the finite difference matrix operator for the 1D model problem u(/d2- f(x) on domain [0, 1] with boundary conditions u(0) = 0 and u(1) = 0, given by [-2 1 1-2 1 E RnXn h2 1 -2 1 This matrix can be considered a discrete version of the continuous operator d/da2 that acts upon a function(r). (a) Show that the n eigenvectors of A are given by the vectors ) (p-1,... , n) with components and with eigenvalues h2...
question 7 9 10
), where n, a, and are constant, is an eigenfunction of p. 7. (a) p. =- what is p. ? (b) sin( i ax what is the eigenvalue? (107) (9) = v ydt for a normalized wavefunction. Please find (1) for(a) v. - and (b) 42p. 4/2008 re s in sind. (hint : integrate over all space: sin Odrdodø (sin? xdx = [l-c952de, 5 xede = (203) 3 2 10. A particle of mass m is...
Please answer number 8
l Verizon LTE 9:53 PM 100%,--+ Close Physical Chemistry ll Spring...1 DOCX-149 KB (e) none of the above 7. A free particle is inside a one dimentional box from 0 to a/2, (a is a constant). If the particle is in the first excited states with eigenfunction, y Nsin (4px/a) (a) Determine the normalization constant. (b) Calculate the probability in between a/4 and a/2 8. What is the degree of the degeneracy if the three quantum...
1) (35 points) The wave function for a particle moving along x axis between the limits 0 and L is: (x)-C sin (nx xL) where n are 1, 2, 3, A) Determine the normalization constant C B) Why can't n take the value of 0, briefly explain C) For n-3 determine the values of x (in terms of L) that correspond to a maximum or a minimum in the wave function D) For n-3 determine the values of x (in...
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