# Energy of a particle near a potential well

1. Apr 25, 2015

### 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

2. Apr 25, 2015

### The_Duck

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.

3. Apr 27, 2015

### Urmi Roy

Thanks, that makes sense :-)