Question: When determining the partition function for the harmonic oscillator, the zero-point energy of the oscillator was ignored. Show that the expression for the probability of

When determining the partition function for the harmonic oscillator, the zero-point energy of the oscillator was ignored. Show that the expression for the probability of occupying a specific energy level of the harmonic oscillator with the inclusion of zero-point energy is identical to that ignoring zero-point energy.

Step by Step Solution

★★★★★

3.28 Rating (163 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

Beginning with the energy of each level of the harmonic oscillator including zeropoint e... View full answer

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Physical Chemistry Questions!

What is the phase constant for the harmonic oscillator with the velocity function v(t) given in Figure if the position function x(t) has the form x = x- cos (wt + )? The vertical axis scale is set by...

a. In this chapter, the assumption was made that the harmonic oscillator model is valid such that anharmonicity can be neglected. However, anharmonicity can be included in the expression for...

True or false? (a) All harmonic-oscillator wave functions with v an odd integer must have a node at the origin. (b) The v = 10 harmonic-oscillator wave function has 10 interior nodes. (c) The v = 1...

In our statistical treatments of quantum systems, we typically neglect any zero-point energy (i.e. we always assume that the energy of the ground state is zero). Show that the expression for the...

please help me solve these questions, the teacher included the final answer in the screenshots but I want the steps for it so I can understand how they got the final answer ( that's all screenshot so...

In constructing the vibrational partition function, we found that the definition depended on whether zero-point energy was included in the description of the energy levels. However, the expression...

The Boltzmann equation gives the probability of finding a system in the state n (with energy E n ), at temperature T(k B is Boltzmann's constant). The probability here refers to the random thermal...

Please look into the problems below: Alright, people, let's do this one last time! Consider again a paramagnet system of N spins in a magnetic field B. We will use the symbol to denote a microstate...

data Structures and Other Objects Using C++ Second Edition by Michael Main and Walter Savitch C++ Header File// // PROVIDES: A better quicksort function:\ // void quicksort(\ // void* base,\ //...

In our analysis of hydrogen in Chap. 9, we discussed the period of recombination, the time in the history of the universe at which protons and electrons became bound and formed neutral hydrogen. We...

Jill's Gloves (JG) is a sole trader owned by Jill McAloon. The business makes and sells ski gloves. JG sells each pair of gloves for $20. Jill has forecasted sales in 2022 to be 20 000 units. She has...

1.In life insurance, what are trailing commissions ? a. Commissions on life insurance policies after the first year. b. Commissions on only term life insurance policies. c. Commissions on only...

2. The manager of an automobile dealership is considering a new bonus plan designed to increase sales volume. Currently, the mean sales volume is 14 automobiles per month. The manager wants to...

c. Draw a diagram to illustrate your answer to part a.

Calculate the thermal conductivity of argon (C V,m =12.5 JK 1 mol 1 , =0.36nm 2 ) at 298K.

The viscosity of benzene varies with temperature as shown in the following table. Use the data to infer the activation energy for viscosity. /lC n/cP 10 0.758 20 30 40 50 0.652 0.564 0.503 0.442 60...

Explain how Ficks first law arises from the concentration gradient of gas molecules.

Question: At whatever point a driver experiences slowing down issues, particularly an erratic pulling aside, the scoundrel is constantly held to be the brake cushion. Minor components, particularly...

A review of univariate normal inference theory: consider X1, ,Xn a random sample from an assumed normal distribution with unknown mean y. We want to test the hypothesis H0: p = {.10 and Ha: ,u at #0...

Use technology to find (a) the multiple regression equation for the data shown in the accompanying table, (b) the standard error estimate and interpret the result, and (c) the coefficient of...