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I wonder how <0|a_(a+a_ + a_a+)a+|0> = <0|(a_a+ + 2a_a+)|0> = 3??. Here <0| is the (unperturbed) ground state level of an anharmonic oscillator and a+ is the creation operator and a_ is the annihilation operator.
I would get from <0|a_(a+a_ + a_a+)a+|0> that this becomes:
<0|a_a+a_a+ + (a_)^2(a+)^2|0> or
<0|a_a+a_a+ + (a_)(a_)(a+)(a+)|0>.
How in the world could this equal to <0|(a_a+ + 2a_a+)|0> = 3
could anyone give a qualitative reason for this?
kind regards
I would get from <0|a_(a+a_ + a_a+)a+|0> that this becomes:
<0|a_a+a_a+ + (a_)^2(a+)^2|0> or
<0|a_a+a_a+ + (a_)(a_)(a+)(a+)|0>.
How in the world could this equal to <0|(a_a+ + 2a_a+)|0> = 3
could anyone give a qualitative reason for this?
kind regards
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