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Unformatted text preview: . Solutions of this form correspond to states with definite energy since H op  > = E > . Substituting (x,t) into the time dependent equation yields ) ( ) ( 2 1 ) ( 2 2 2 2 2 x E x Kx dx x d m = + h and hence ) ( 2 2 ) ( 2 2 2 2 2 = + x x mf mE dx x d h h where I set K = m(2 f) 2 . Setting h / 2 mf = and 2 / 2 h mE = yields ) ( ) ( ) ( 2 2 2 2 = + x x dx x d . We must find the allowed solutions ( i.e. (x) must be squareintegrable) of this differential equation. The differential equation can be converted into the Hermite Differential Equation and the solutions are Hermite Polynomials . We will not solve for the energy levels in this way, instead we will solve the problem using operators!...
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 Spring '07
 FIELDS
 mechanics, Force

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