Fund Quantum Mechanics Lect & HW Solutions 48

Fund Quantum Mechanics Lect & HW Solutions 48 - 3 2...

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30 CHAPTER 3. BASIC IDEAS OF QUANTUM MECHANICS 3.6.2.4 Solution harmb-d Question: Write out the eigenstate ψ 100 fully. Answer: Taking the generic expression ψ n x n y n z = h n x ( x ) h n y ( y ) h n z ( z ) and substituting n x = 1, n y = n z = 0, you get ψ 100 = h 1 ( x ) h 0 ( y ) h 0 ( z ) . Now substitute for h 0 and h 1 from table 3.1: ψ 100 = 2 x/ℓ ( πℓ 2 ) 3 / 4 e x 2 / 2 2 e y 2 / 2 2 e z 2 / 2 2 where the constant is as given in table 3.1. You can multiply out the exponentials: ψ 100 = 2 x/ℓ ( πℓ 2 ) 3 / 4 e ( x 2 + y 2 + z 2 ) / 2 2 . 3.6.3 Discussion of the eigenvalues
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Unformatted text preview: 3 2 h 5 2 h 7 2 h 9 2 h n x = n y = n z = n x = 1 0 0 n y = 0 1 0 n z = 0 0 1 n x = 2 0 0 1 1 0 n y = 0 2 0 1 0 1 n z = 0 0 2 0 1 1 n x = 3 0 0 2 0 1 0 2 1 1 n y = 0 3 0 1 2 0 1 0 2 1 n z = 0 0 3 0 1 2 2 1 0 1 Figure 3.3: The energy spectrum of the harmonic oscillator....
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This note was uploaded on 01/06/2012 for the course PHY 3604 taught by Professor Dr.danielarenas during the Fall '11 term at UNF.

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