The Hamiltonian operator Ĥ for the harmonic oscillator is given by Ĥ = h d? + uw? â2, where u is the reduced mass and w = 2TV is the angular 2µ dæ? frequency. Is the function f() = x exp an eigenfunction of that Hamiltonian? 2h

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问题6
The Hamiltonian operator Ĥ for the harmonic oscillator is given by
h d?
+ uw? â2, where u is the reduced mass and w = 2Tv is the angular
2µ da?
frequency. Is the function f(x) = x exp-
iwa?
an eigenfunction of that Hamiltonian?
2h
O No.
Yes, and the eigenvalue is hw.
Yes, and the eigenvalue is hw.
3ħw
Yes, and the eigenvalue is
4
Transcribed Image Text:问题6 The Hamiltonian operator Ĥ for the harmonic oscillator is given by h d? + uw? â2, where u is the reduced mass and w = 2Tv is the angular 2µ da? frequency. Is the function f(x) = x exp- iwa? an eigenfunction of that Hamiltonian? 2h O No. Yes, and the eigenvalue is hw. Yes, and the eigenvalue is hw. 3ħw Yes, and the eigenvalue is 4
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