3 Quantum Harmonic Oscillator Another form of a potential energy function that can be used to describe a molecular bond is: V(y) = where and are constants. (A) Using a Taylor Series expansion, derive an effective harmonic force constant that could be used for a harmonic oscillator approximation to the potential V(y) around the point y=0. (B) What are the eigenvalues of the QHO Hamiltonian utilizing the harmonic force constant you derived in (A)? (C) Calculate for the n-3 QHO wavefunction. You must work through the math to show your solution (either Mathematica or even/odd function relationships are suitable means of evaluating integrals). (D) Calculate for the n=3 QHO wavefunction. You must work through the math to show your solution (either Mathematica or even/odd function relationships are suitable means of evaluating integrals). (E) Calculate the commutator of [H,py] (be sure you include all terms in the QHO Hamiltonian). What does your result mean about the ability to measure H and Py simultaneously? Evaluate the following expressions numerically: <1|PrV3 >, < 2P1516 >, (F) <448|23|452>
3 Quantum Harmonic Oscillator Another form of a potential energy function that can be used to describe a molecular bond is: V(y) = where and are constants. (A) Using a Taylor Series expansion, derive an effective harmonic force constant that could be used for a harmonic oscillator approximation to the potential V(y) around the point y=0. (B) What are the eigenvalues of the QHO Hamiltonian utilizing the harmonic force constant you derived in (A)? (C) Calculate for the n-3 QHO wavefunction. You must work through the math to show your solution (either Mathematica or even/odd function relationships are suitable means of evaluating integrals). (D) Calculate for the n=3 QHO wavefunction. You must work through the math to show your solution (either Mathematica or even/odd function relationships are suitable means of evaluating integrals). (E) Calculate the commutator of [H,py] (be sure you include all terms in the QHO Hamiltonian). What does your result mean about the ability to measure H and Py simultaneously? Evaluate the following expressions numerically: <1|PrV3 >, < 2P1516 >, (F) <448|23|452>
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Please do not rely too much on chatgpt, because its answer may be wrong. Please consider it carefully and give your own answer. You can borrow ideas from gpt, but please do not believe its answer.Very very grateful!Please do not rely too much on chatgpt, because its answer may be wrong. Please consider it carefully and give your own answer. You can borrow ideas from gpt, but please do not believe its answer.
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And please do not copy other's work!Thanks!!!
And please do not copy other's work!Thanks!!!
![3 Quantum Harmonic Oscillator
Another form of a potential energy function that can be used to describe a molecular bond is:
V(y)
=
where and are constants.
(A)
Using a Taylor Series expansion, derive an effective harmonic force constant that
could be used for a harmonic oscillator approximation to the potential V(y) around the point y=0.
(B)
What are the eigenvalues of the QHO Hamiltonian utilizing the harmonic force
constant you derived in (A)?
(C)
Calculate <y> for the n-3 QHO wavefunction. You must work through the
math to show your solution (either Mathematica or even/odd function relationships are suitable
means of evaluating integrals).
(D)
Calculate <py > for the n=3 QHO wavefunction. You must work through the
math to show your solution (either Mathematica or even/odd function relationships are suitable
means of evaluating integrals).
(E)
Calculate the commutator of [H,py] (be sure you include all terms in the QHO
Hamiltonian). What does your result mean about the ability to measure H and Py simultaneously?
Evaluate the following expressions numerically: <1|PrV3 >, < 2P1516 >,
(F)
<448|23|452>](https://content.bartleby.com/qna-images/question/b924e824-f7b8-486a-bee8-48b1feb67b77/001cd7cd-e1d7-4806-93a2-8cb7e7f3c3ee/dsg5jzo_processed.png)
Transcribed Image Text:3 Quantum Harmonic Oscillator
Another form of a potential energy function that can be used to describe a molecular bond is:
V(y)
=
where and are constants.
(A)
Using a Taylor Series expansion, derive an effective harmonic force constant that
could be used for a harmonic oscillator approximation to the potential V(y) around the point y=0.
(B)
What are the eigenvalues of the QHO Hamiltonian utilizing the harmonic force
constant you derived in (A)?
(C)
Calculate <y> for the n-3 QHO wavefunction. You must work through the
math to show your solution (either Mathematica or even/odd function relationships are suitable
means of evaluating integrals).
(D)
Calculate <py > for the n=3 QHO wavefunction. You must work through the
math to show your solution (either Mathematica or even/odd function relationships are suitable
means of evaluating integrals).
(E)
Calculate the commutator of [H,py] (be sure you include all terms in the QHO
Hamiltonian). What does your result mean about the ability to measure H and Py simultaneously?
Evaluate the following expressions numerically: <1|PrV3 >, < 2P1516 >,
(F)
<448|23|452>
