0
votes
0answers
74 views

Prove that the position operator is $\hat{x} = i\hbar \frac{d}{{dp}}$ in the momentum representation [closed]

Proof that: $x = i\hbar \frac{d}{{dp}}$ I did this, could you tell me if I am false or true $\begin{array}{l} x{e^{\frac{{ipx}}{\hbar }}} = - i\hbar \frac{{d{e^{\frac{{ipx}}{\hbar }}}}}{{dp}} = ...
2
votes
0answers
34 views

Difficulty in obtaining the Lorentzian lineshape for natural broadening [migrated]

Not sure if this maybe belongs more in the maths section, but since it comes from a physics problem i'll post here. when calculating the natural broadening lineshape for a laser we have to take the ...
3
votes
2answers
143 views

A four-dimensional integral in Peskin & Schroeder

The following identity is used in Peskin & Schroeder's book Eq.(19.43), page 660: ...
0
votes
1answer
335 views

Gaussian wave packet

At our QM intro our professor said that we derive uncertainty principle using the integral of plane waves $\psi = \psi_0(k) e^{i(kx - \omega t)}$ over wave numbers $k$. We do it at $t=0$ hence $\psi = ...
1
vote
2answers
289 views

Finding $\psi(x)$ from Fourier modes

In quantum physics we've defined: $$ \psi (x) = \sqrt{ \dfrac{1}{2 \pi \hbar} } \int^{ \infty }_{-\infty } \phi (p) \exp \left( i \dfrac{px}{ \hbar} \right) dp $$ Now, $$a(k) \equiv \sqrt{ \hbar } ...