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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)

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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Va = (2a³ – 3x) exp(-x²/2). 3æ) exp(-2²/2). || |
Transcribed Image Text:Va = (2a³ – 3x) exp(-x²/2). 3æ) exp(-2²/2). || |
1 ÂĤ = ââ + H 2'
Transcribed Image Text:1 ÂĤ = ââ + H 2'
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