1)energy levels. In particular, sketch the wavefunctions that correspond to the lowest 4 energy levels.For a particle in a 1D box that has length of b, sketch the wave functions that correspond to discrete

As energy levels increses the energy gap between levels increases.

Answered: 1) energy levels. In particular, sketch…

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 10.16E: A particle on a ring has a wavefunction =12eim where equals 0 to 2 and m is a constant. Evaluate...

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Similar questions

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.
An electron is confined to a box of dimensions 2A3A5A. Determine the wavefunctions for the five lowest energy states.
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?
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 =12eim where equals 0 to 2 and m is a constant. Evaluate the angular momentum p of the particle if p=i How does the angular momentum depend on the constant m?
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.
State whether the following functions are acceptable wavefunctions over the range given. If they are not, explain why not. a=ex2,x+ bF(x)=sin4x,x cx=y2,x0 dThe function that looks like this: eThe function that looks like this:
For an unbound or free particle having mass m in the complete absence of any potential energy that is, V=0, the acceptable one-dimensional wavefunctions are =Aei(2mE)1/2x/h+Bei(2mE)1/2x/h, where A and B are constants and E is the energy of the particle. Is this wavefunction normalizable over the interval x+? Explain the significance of your answer.
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.
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?
An official baseball has a mass of 145g. a Assuming that a baseball in New Orleans Superdome width =310m is acting as a particle-in-a-box, what is its energy in the n=1 state? b Assuming that the energy in part a is all kinetic energy (=12mv2), what is the velocity of the baseball in the n=1 state? c A hit baseball can travel as fast as 44.7m/s. Calculate the classical kinetic energy of the hit baseball and, assuming that this energy is quantized, determine the quantum number of the hit baseball.

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1) energy levels. In particular, sketch the wavefunctions that correspond to the lowest 4 energy levels. For a particle in a 1D box that has length of b, sketch the wave functions that correspond to discrete