#### Question Details

This is physical Chemistry Homework Problems. Please see attachment.

1. Consider a collection of distinguishable andindependent (i.e. non-interacting) harmonicoscillators, all with the same characteristic frequency . If there are 4oscillators in the collection,how many Hamiltonian eigenstatesare there with a total system energy less thanor equal to 8?w?What about 8 oscillators and 16?w? What about 12 oscillators and 24?w?

2.Using your results from question 1, explain why it would be extremely difficult to find the exact ground state in a large collection of oscillators that interacted with each other.

3. Consider the lowest energy triplet state (in which both electrons are spin up) of the hydrogenmolecule for a bond distance of 0.75bohr.Inspired by mean field theory, you decide to construct as your approximate wave function a Slater determinant in which the two molecular orbitals are the +and ?linear combinations of the hydrogen atom 1s orbitals centered on each of the two nuclei. Assuming both electrons lie on the internuclear axis and that one of them is held fixed 1/6of the wayin between the nuclei, evaluate the probabilities of finding the other electron 0/9, 1/9, 2/9, ?, up to8/9 of the way in between the nuclei relative to finding it at the far nucleus(i.e. at 9/9). Explain whatyou see in your results.

Hint: When computing relative probabilities (i.e. ratios of probabilities), the normalization of the wave function does not matter.

Chem 120A, Fall 2015 Problem Set 10 Due in G08 Gilman on Dec 9 at 3pm 1. Consider a collection of distinguishable and independent (i.e. non-interacting) harmonic oscillators, all with the same characteristic frequency . If there are 4 oscillators in the collection, how many Hamiltonian eigenstates are there with a total system energy less than or equal to 8?? What about 8 oscillators and 16?? What about 12 oscillators and 24?? 2. Using your results from question 1, explain why it would be extremely difficult to find the exact ground state in a large collection of oscillators that interacted with each other. 3. Consider the lowest energy triplet state (in which both electrons are spin up) of the hydrogen molecule for a bond distance of 0.75 bohr. Inspired by mean field theory, you decide to construct as your approximate wave function a Slater determinant in which the two molecular orbitals are the + and ? linear combinations of the hydrogen atom 1s orbitals centered on each of the two nuclei. Assuming both electrons lie on the internuclear axis and that one of them is held fixed 1/6 of the way in between the nuclei, evaluate the probabilities of finding the other electron 0/9, 1/9, 2/9, ?, up to 8/9 of the way in between the nuclei relative to finding it at the far nucleus (i.e. at 9/9). Explain what you see in your results. Hint: When computing relative probabilities (i.e. ratios of probabilities), the normalization of the wave function does not matter.

**Solution details:**

Answered

QUALITY

Approved

ANSWER RATING

This question was answered on: * Jan 30, 2021 *

* * Solution~0001017576.zip (25.37 KB)

This attachment is locked

We have a ready expert answer for this paper which you can use for in-depth understanding, research editing or paraphrasing. You can buy it or order for a fresh, original and plagiarism-free solution (Deadline assured. Flexible pricing. TurnItIn Report provided)

##### Pay using PayPal (No PayPal account Required) or your credit card . All your purchases are securely protected by .

#### About this Question

STATUSAnswered

QUALITYApproved

DATE ANSWEREDJan 30, 2021

EXPERTTutor

ANSWER RATING

#### GET INSTANT HELP/h4>

We have top-notch tutors who can do your essay/homework for you at a reasonable cost and then you can simply use that essay as a template to build your own arguments.

You can also use these solutions:

- As a reference for in-depth understanding of the subject.
- As a source of ideas / reasoning for your own research (if properly referenced)
- For editing and paraphrasing (check your institution's definition of plagiarism and recommended paraphrase).

#### NEW ASSIGNMENT HELP?

### Order New Solution. Quick Turnaround

Click on the button below in order to Order for a New, Original and High-Quality Essay Solutions.
New orders are original solutions *and precise to your writing instruction requirements. Place a New Order using the button below.*

WE GUARANTEE, THAT YOUR PAPER WILL BE WRITTEN FROM SCRATCH AND WITHIN A DEADLINE.