The Hamiltonian of a one-dimensional harmonic oscillator can be written in natural units (m = hbar= ω = 1) as: (image1) Where ˆa =(ˆx+ipˆ)/√2, and ˆa† =(ˆx−ipˆ)/√2 One of the proper functions is: (image2) Find the two eigenfunctions closest in energy to the function ψa (you don't have to normalize)
The Hamiltonian of a one-dimensional harmonic oscillator can be written in natural units (m = hbar= ω = 1) as: (image1) Where ˆa =(ˆx+ipˆ)/√2, and ˆa† =(ˆx−ipˆ)/√2 One of the proper functions is: (image2) Find the two eigenfunctions closest in energy to the function ψa (you don't have to normalize)
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The Hamiltonian of a one-dimensional harmonic oscillator can be written in natural units (m = hbar= ω = 1) as: (image1)
Where ˆa =(ˆx+ipˆ)/√2, and ˆa† =(ˆx−ipˆ)/√2
One of the proper functions is: (image2)
Find the two eigenfunctions closest in energy to the function ψa (you don't have to normalize)
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3æ) exp(-2²/2).
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Transcribed Image Text:1
ÂĤ = ââ +
H
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