A particle of mass m moves on the x-axis under the influence of the potential $$V(x)=\frac{1}{2}m\omega^2x^2+Fx$$ Can anyone help me, using Schrödinger's equation in one dimension that the energy levels are: $$E_n=(n+\frac{1}{2})h\omega-\frac{1}{2}\frac{F^2}{m\omega^2}$$ Where n is a non negative integer?
Tell me more
×
Physics Stack Exchange is a question and answer site for
active researchers, academics and students of physics. It's 100% free, no registration required.
|
|
||||
|
closed as too localized by David Zaslavsky♦ Feb 12 '12 at 2:41
This question is unlikely to help any future visitors; it is only relevant to a small geographic area, a specific moment in time, or an extraordinarily narrow situation that is not generally applicable to the worldwide audience of the internet. For help making this question more broadly applicable, see the FAQ.
|
$V(x)=\frac{1}{2}m\omega^2x^2+Fx=\frac{1}{2}m\omega^2(x^2+\frac{2F}{m\omega^2}x)=\frac{1}{2}m\omega^2((x+\frac{2F}{m\omega^2})^2-\frac{F^2}{m^2\omega^4})=\frac{1}{2}m\omega^2x'^2-\frac{1}{2}\frac{F^2}{m\omega^2}$ and you have, that it is potential of the oscillator minus constant. So energy levels offset by this constant. |
|||
|
|
|
Try a change of coordinates $x\rightarrow x-x_0$, where $x_0$ is an appropriate constant. |
|||
|
|
