[Quantum Mechanics] Anharmonic oscillator

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Typeset text on the one-dimensional harmonic oscillator with Hamiltonian H = ħω(½p² + ½ξ² + kξ⁴) and energy spacing E(n+1) − E(n) = ħω, followed by the first-order correction E'n = En + kħω<n|ξ⁴|n> + ....


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?
 
I found a solution : )

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