The Hamiltonian for a harmonic oscillator can be written in dimension- less units (m = h = w = 1) as Ĥ = âtâ + 1/2, where â = (î + ip)//2, ât = (± – ip)/V2. %3D %3D One unnormalized energy eigenfunction is Va = (2x – 3x) exp (-r²/2). %3D Find two other (unnormalized) eigenfunctions which are closest in en- ergy to va.
The Hamiltonian for a harmonic oscillator can be written in dimension- less units (m = h = w = 1) as Ĥ = âtâ + 1/2, where â = (î + ip)//2, ât = (± – ip)/V2. %3D %3D One unnormalized energy eigenfunction is Va = (2x – 3x) exp (-r²/2). %3D Find two other (unnormalized) eigenfunctions which are closest in en- ergy to va.
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Transcribed Image Text:The Hamiltonian for a harmonic oscillator can be written in dimension-
less units (m = h = w = 1) as
Ĥ = âtâ + 1/2,
where
â = (îr + ip)/v2, ât = (â – ip)/V2.
%3D
%3D
One unnormalized energy eigenfunction is
Va = (2x – 3x) exp(-x²/2).
Find two other (unnormalized) eigenfunctions which are closest in en-
ergy to fa.
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