Quantum Mechanics Answers

Firstly, from spectral lines, it is said that an electron going around a nucleus can not be in between energy levels, in that it must be in one or another of these allowed orbits, but if it moves from one energy level to another, there must be a small amount of time in which it is in between these energy levels. If that is true (which it must be because of relativity), how long does it spend in between these levels, or is it impossible to determine that to a very high degree of accuracy because of the uncertainty principle?

An x-ray photon of the maximum energy produced by a tube leaves the tube and collides elastically with an electron at rest. As a result, the electron recoils and the x-ray is scattered. The frequency of the scattered x-ray photon is 1.64x10^19Hz. Relativistic effects may be neglected for the electron.
Determine the kinetic energy of the recoiled electron and the magnitude of its momentum.

Hi
I would like to know that how can we write the commutation between Pj and a field?
I know the answer is "-ih d(field)/dx" but as Pj is in integral form I don't know how to prove it!
It's actually problem 2.4 of "quantum field theory " by mandle
thanks!

Prove that if the operator A^ is Hermitian, then the operator A^n is also Hermitian. (n is a positive integer).

How will the full wave function Ψ(x, t), which describes the stationary states, change if you change the origin of the potential energy at some value of ΔU?

Show that the γ-quantum can not form a pair outside the nucleus field, even if such process is energetically possible.

Prove that if the operator A^ is Hermitian, its eigenvalues are real.

How will the full wave function Ψ(x, t), which describes the stationary states, change if you change the origin of the potential energy at some value of ΔU?

A free electron in the initial moment was localized in an area with the size l = 10^(-8) cm. Estimate the period for which the width of the wave packet will increase in η = 10² times.

Freely moving non-relativistic particle has a relative uncertainty of the kinetic energy of about 1.6 ∙ 10^(-4). Estimate how much the coordinate uncertainty of such particle is bigger than its de Broglie wavelength.