Physical chemistry: Quantum Mechanics Consider a particle in the following 1D box. The potential in this box has the form:1Vkx?For a particle in a square box with infinite height the wavefunction and energies are:n²h?E°8mL?with1/22плхsina. Calculate the first order perturbation of energy for this potential using the abovewavefunction and energies as the unperturbed values.b. Calculate the first order wavefunction

Answered: Image /qna-images/answer/51a37beb-c6d2-492f-ad6d-85313c366a28.jpg

Consider a particle in the following 1D box. The potential in this box has the form: 1 2. V = kx² 2 For a particle in a square box with infinite height the wavefunction and energies are: n²h? E° 8mL? with 1/2 sin() плх a. Calculate the first order perturbation of energy for this potential using the above wavefunction and energies as the unperturbed values. b. Calculate the first order wavefunction

Consider a particle in the following 1D box. The potential in this box has the form: 1 2. V = kx² 2 For a particle in a square box with infinite height the wavefunction and energies are: n²h? E° 8mL? with 1/2 sin() плх a. Calculate the first order perturbation of energy for this potential using the above wavefunction and energies as the unperturbed values. b. Calculate the first order wavefunction

Physical Chemistry

2nd Edition

ISBN:9781133958437

Author:Ball, David W. (david Warren), BAER, Tomas

Publisher:Ball, David W. (david Warren), BAER, Tomas

Chapter10: Introduction To Quantum Mechanics

Section: Chapter Questions

Problem 10.57E: Is the uncertainty principle consistent with our description of the wavefunctions of the 1D...

See similar textbooks

Similar questions

What is the physical explanation of the difference between a particle having the 3-D rotational wavefunction 3,2 and an identical particle having the wavefunction 3,2?
For a particle in a state having the wavefunction =2asinxa in the range x=0toa, what is the probability that the particle exists in the following intervals? a x=0to0.02ab x=0.24ato0.26a c x=0.49ato0.51ad x=0.74ato0.76a e x=0.98ato1.00a Plot the probabilities versus x. What does your plot illustrate about the probability?
A particle on a ring has a wavefunction =eim, where =0to2 and m is a constant. a Normalize the wavefunction, where d is d. How does the normalization constant depend on the constant m? b What is the probability that the particle is in the ring indicated by the angular range =0to2/3? Does this answer make sense? How does the probability depend on constant m?
Is the uncertainty principle consistent with our description of the wavefunctions of the 1D particle-in-a-box? Hint: Remember that position is not an eigenvalue operator for the particle-in-a-box wavefunctions.
Show that the normalization constants for the general form of the wavefunction =sin(nx/a) are the same and do not depend on the quantum number n.
Why does the wavefunction 4,4,0 not exist? Similarly, why does a 3f subshell not exist? See exercise 11.73 for notation definition.
Spin orbitals are products of spatial and spin wavefunctions, but correct antisymmetric forms of wavefunctions for multielectron atoms are sums and differences of spatial wavefunctions. Explain why acceptable antisymmetric wavefunctions are sums and differences that is, combinations instead of products of spatial wavefunctions.
Based on the trend shown in Figure 11.5, draw the probability distribution of a harmonic oscillator wavefunction that has a very high value of n. Explain how this is consistent with the correspondence principle.
What is the degeneracy of an h subshell? An n subshell?
In exercise 10.41a, the wavefunction is not normalized. Normalize the wavefunction and verify that it still satisfies the Schrdinger equation. The limits on x are 0 and 2. How does the expression for the energy eigenvalue differ?
Verify that the following wavefunctions are indeed eigenfunctions of the Schrdinger equation, and determine their energy eigenvalues. a =eiKx where V=0 and K is a constant b =eiKx where V=k, k is some constant potential energy, and K is a constant c =2asinxa where V=0.
The uncertainty principle is related to the order of the two operators operating on a wavefunction. Evaluate the expressions x (pxsinx) and px( x sinx) and demonstrate that you get different results.