The Hamiltonian operator y for the harmonic oscillator is given by Ĥ = - a h? d? + suw? â?, where l is the reduced mass and w = 27V is the angular 2µ dæ? pwx frequency. Is the function f(x) = x exp an eigenfunction of that Hamiltonian? 2h O No. Yes, and the eigenvalue is ħw. 2 O Yes, and the eigenvalue is hw. 3hw Yes, and the eigenvalue is 4
The Hamiltonian operator y for the harmonic oscillator is given by Ĥ = - a h? d? + suw? â?, where l is the reduced mass and w = 27V is the angular 2µ dæ? pwx frequency. Is the function f(x) = x exp an eigenfunction of that Hamiltonian? 2h O No. Yes, and the eigenvalue is ħw. 2 O Yes, and the eigenvalue is hw. 3hw Yes, and the eigenvalue is 4
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 10.40E
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Question
![The Hamiltonian operator y for the harmonic oscillator is given by
 =
h? d?
+ suw? â?, where l is the reduced mass and w = 27V is the angular
2µ dæ?
P[-]
pwx?
frequency. Is the function f(x) = x exp
an eigenfunction of that Hamiltonian?
2h
O No.
Yes, and the eigenvalue is ħw.
2
Yes, and the eigenvalue is hw.
3ħw
Yes, and the eigenvalue is
4](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0c5bfc5d-3b7f-4351-8bf4-a98928c68bf4%2F6a168f29-c127-463e-8cfb-7b2c5d428fe3%2Fstrk8ki_processed.png&w=3840&q=75)
Transcribed Image Text:The Hamiltonian operator y for the harmonic oscillator is given by
 =
h? d?
+ suw? â?, where l is the reduced mass and w = 27V is the angular
2µ dæ?
P[-]
pwx?
frequency. Is the function f(x) = x exp
an eigenfunction of that Hamiltonian?
2h
O No.
Yes, and the eigenvalue is ħw.
2
Yes, and the eigenvalue is hw.
3ħw
Yes, and the eigenvalue is
4
Expert Solution
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Step 1
Given:
Hamiltonian operator
is the reduced mass
is the angular frequency
To find: if is an eigenfunction of that Hamiltonian
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