Fund Quantum Mechanics Lect & HW Solutions 46

Fund Quantum Mechanics Lect & HW Solutions 46 - 28...

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Unformatted text preview: 28 3.5.9 3.6 CHAPTER 3. BASIC IDEAS OF QUANTUM MECHANICS Quantum confinement The Harmonic Oscillator 3.6.1 The Hamiltonian 3.6.2 Solution using separation of variables h0 (x) = h1 (x) = h2 (x) = h3 (x) = h4 (x) = 1 (πℓ2 )1/4 e−ξ 2ξ 2 /2 e−ξ 2ξ 2 − 1 e−ξ e−ξ 2 /2 (4πℓ2 )1/4 (9πℓ2 )1/4 4ξ 4 − 12ξ 2 + 3 (576πℓ2 )1/4 c m ℓ= 2 /2 2ξ 3 − 3ξ ω= 2 /2 (4πℓ2 )1/4 h ¯ mω ξ= e−ξ x ℓ 2 /2 Table 3.1: First few one-dimensional eigenfunctions 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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