Momentum space Definition and 69 Threads

Quantum Field Theory Purly in Momentum Space? Hello, I have a complicated nonlinear-nonlocal-nonrelativistic-effective action in momentum space and would like to do perturbation theory with that. I need to find propagator and Feynman rules. I can not go to x-space and follow the standard...

Hi all, I understand how to transform between position space and momentum space; it's a Fourier transform: \varphi|p>=\frac{1}sqrt{2\hbar\pi}\int_{\infty}^{\infty} <x|\varphi> exp(-ipx/\hbar)dx But I can't figure out how to transform the operators. I know what they transform into (e.g...

Hi, I am having trouble understanding some things about k-space or momentum space in a crystal. The trouble began when I was first introduced to the Bloch theorem, a few weeks back. It is: \psi_{n\mathbf{k}}(\mathbf{r})=e^{i\mathbf{k}\cdot\mathbf{r}}u_{n\mathbf{k}}(\mathbf{r}). In...

does anyone knw the code for how to produce the d slash notation in the integration measure for momentum space? Where (d slash)^n X=(d^n)X/((2pi)^n). Basically all i want to do is replace the h: \hslash with a d.

does anyone knw the code for how to produce the d slash notation in the integration measure for momentum space? Where (d slash)^n X=(d^n)X/((2pi)^n). Basically all i want to do is replace the h: \hslash with a d.

Problem Derive the Schroedinger equation (for harmonic oscillator) in momentum space. The attempt at a solution We have ih \frac{\partial}{\partial t} \langle p' | \alpha \rangle = \langle p' | \frac{p^2}{2m} | \alpha \rangle + \langle p' | V(x) | \alpha \rangle \iff ih...

I have learned that to transform from one space to another, we can use g(e) = g(p)/f’, where de/dp = f’ Can we use this relation to transform wavefunctions of energy space to momentum space? If not, why? If so, that's very strange as E= p^2/2m and dE/dp= p/m and put into...

Homework Statement Check that a given momentum space wave function is normalized. I've done the integral, but the result is not dimensionless. Here is the wave function: \overline{\phi} = \frac{1}{\pi} ( \frac{2 a_{0}}{\bar{h}})^{3/2} \frac{1}{(1+(a_{0} p / \bar{h})^2)^2} The units of this...

How can I write the Schrodinger equation for the harm. oscillator in momentum space and then solve it? Thank you, in advance:)

[b]1. The figure shows the rear view of a space capsule that was left rotating about its axis at 6 rev/min after a collision with another capsule. You are the flight controller and have just moments to tell the crew how to stop this rotation before they become ill from the rotation and the...

Page 152 Robinett: Consider the (non-normalized) even momentum space wavefunctions for the symmetric well:, \phi_n^+(p) = 2sin(w-m)/(w-m)+sin(w+m)/(w+m) where w = sin((n-1/2)pi) and m = ap/hbar. Show that \int_{-\infty}^{\infty}\phi_n^+(p)^*\cdot \phi_n^+(p) dp = \delta_{n,m} The hint...

Problem: Find the momentum-space wave function \Phi_n(p,t) for the nth stationary state of the infinite square well. Equations: \Psi_n(x,t) = \psi_n(x) \phi_n(t) \psi_n(x) = \sqrt{\frac{2}{a}}\sin(\frac{n\pi}{a}x) \phi_n(t) = e^{-iE_n t/\hbar} \Phi_n(p,t) =...

Homework Statement Show that <x> = \int \Phi^* \left(-\frac{\hbar}{i}\frac{\partial}{\partial p} \right) \Phi dp Homework Equations \Phi(p,t) = \frac{1}{\sqrt{2\pi\hbar}} \int^{\infty}_{-\infty} e^{\frac{-ipx}{\hbar}} \Psi(x,t)dx \Psi(x,t) = \frac{1}{\sqrt{2\pi\hbar}}...

could somebody please explain to me why position and momentum space are related to one another by a Fourier transform, meaning why do I get momenta when I do a Fourier transform of an expression in position space?

I have this doubt..quantization in momentum space using G(p) as the Fourier transform of the wave function was not common (at least when i studied Q. Physics) my doubt is, if we have that: x |G(p)>=i \hbar \frac{ \partial G(p)}{\partial p} But..what would happen if we apply: \dot...

How exactly does one find a wave function? Specifically, I am asked to find the momentum space wave functoin for the nth stationary state in an infinite square well. Then I am to graph the probability density (phi sqaured) for the first and second energy levels. Lastly, I need to use the...

Hey, We are given the 1s spatial wave function for the hydrogen atom: \psi(\vec{r}) = \frac{1}{\sqrt{a_{0}^3r}}e^{-r/a_{0} We are asked to find the momentum space wave function \phi(\vec{p}). Obviously this is just the Fourier transform of the spatial wave function. In calculating...

I am just starting reading some quantum stuff. There of course be many questions here and there. One thing comes to bother me now that it seems QM are treating this "state" in either momentum or position representation, if leave alone spin space. It seems to treat "momentum" and "position" as...

Please, I would like to write the time-independent schroedinger equation (describing the motion of a bound electron) in momentum space and in cylindrical coordinates. Can you help me? Thank you very much. Hugues Merlain