Particle in 1D Box: What Happens When Wall Removed?

[jayanth]

A particle is moving in a 1D box with infinitely high walls. The potential is zero inside and infinite outside. What will happen if one of the walls is suddenly removed??

 

[Vanadium 50]

Is this coursework?

 

[Naty1]

Seems like insufficient information.

 

[eaglelake]

A particle is moving in a 1D box with infinitely high walls. The potential is zero inside and infinite outside. What will happen if one of the walls is suddenly removed??

First you must know the wavefunction for the infinite well. At the instant the wall is removed you still have the same wavefunction. Assuming you intend to measure the energy in the new configuration, you follow the usual procedure: determine the new energy eigenfunctions and new energy eigenvalues, i.e. solve the eigenvalue equation in the new configuration, and then write the wavefunction in terms of the new eigenfunctions. You now know the possible results of a measurement (the eigenvalues) and the probability of obtaining each result is $$\left| {\left\langle {{E_k }}<br /> \mathrel{\left | {\vphantom {{E_k } \psi }}<br /> \right. \kern-\nulldelimiterspace}<br /> {\psi } \right\rangle } \right|^2$$, where $$\varphi (x) = \left\langle {x}<br /> \mathrel{\left | {\vphantom {x {E_k }}}<br /> \right. \kern-\nulldelimiterspace}<br /> {{E_k }} \right\rangle$$ are the energy eigenfunctions.

Best wishes