Tagged Questions
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 } ...
