Someone please tell me if I am thinking right:(adsbygoogle = window.adsbygoogle || []).push({});

Let's consider an unperturbed electronic state of an atom/molecule. If we denote it by [a>, then the average electronic momentum in state [a> is,

<p> = <a]p[a> = (<a]p<a])* (because p is hermitian)

= (<a]*p*[a>*)

= (<a]p*[a>) (because [a> is real.)

= - (<a]p[a>) ( because p is purely imaginary. so p* = -p)

so, <p> = 0

so, the average momentum in any unperturbed eigenstate = 0

Now, the atom/molecule is being perturbed by a time-dependent scalar potential of the form V(t) = V Cos(wt). So we can write the time-dependent wave function as a perturbation series. Since there is no magnetic field, the wave function will be real and <p> = 0.

Is it true? Please correct me if I am doing it wrong. Thanks.

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# Average electronic momentum in bound state: please see this

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