[Quantum Mechanics] Anharmonic oscillator

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Start date Sep 18, 2014
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Mechanics Oscillator Quantum mechanics

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To compute the expectation value <n|ξ^4|n> for an anharmonic oscillator, the ladder operators a+ and a- are utilized. The expression for ξ is defined as ξ = (a+ + a-) * sqrt(mw/2h). By applying the ladder operators to the state φ, the calculation can be simplified. A specific solution approach is suggested, focusing on manipulating the terms involving the ladder operators. This method provides a pathway to effectively compute the desired expectation value.

Sep 18, 2014

aiaiaial

how to compute <n|ξ^4|n>?

The problem is above
I guess the ladder operator becomes some very ugly term. There should be a trick to compute <n|ξ^4|n>. Could anyone tell me?

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Sep 18, 2014

aiaiaial

I found a solution : )

just start with ξ = (a+ + a-) * sqrt(mw/2h)
and keep dealing with (a+)φ and (a-)φ.

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