Energy of a particle near a potential well

[Urmi Roy]

Hi All,

During our Quantum Mechanics class one of the students asked if it was possible for a particle to enter a region (just before a potential well) with a negative energy. The TA said that the energy could be negative, but if the potential well has it's bottom at -U (where U is some positive number), the particle's energy can't be less than that.

I'm wondering however, in reference to the situation with a potential barrier, since a particle with energy E>U' (where U' is the energy of potential barrier) has an exponentially decaying wave function inside the barrier, the particle with energy lower than the potential well would similarly have an exponentially decaying wave function in the well.

Does this sound correct?

Thanks!
-Urmi

 

[The_Duck]

I'm wondering however, in reference to the situation with a potential barrier, since a particle with energy E>U' (where U' is the energy of potential barrier) has an exponentially decaying wave function inside the barrier, the particle with energy lower than the potential well would similarly have an exponentially decaying wave function in the well.

Does this sound correct?

Sure. The problem is that the wave function has to be normalizable. If you try to write down a wave function with energy less than the minimum of the potential, it looks like an exponential everywhere, and you will find that such a function is not normalizable.

 

[Urmi Roy]

Thanks, that makes sense :-)