Bound state of the delta function potential.

[siddharth5129]

What is the physical meaning to a bound state with negative energy? As I understand it, this is the case with the delta function potential, which admits only one bound state with a negative energy.
If the potential function is identically zero throughout (except at the delta function peak), doesn't this translate to a system with a negative kinetic energy? What am I missing here ?

 

[Nugatory]

The zero point of potential energy is arbitrary, so there's no physical significance to a negative energy; negative just means it's less than the energy at whatever we've chosen to be zero. It's a very common, very convenient, convention to choose the zero point so that all the bound states are below it, hence are negative.

This isn't QM, potentials in classical physics work the same way.

 

[DrDu]

Kinetic energy is infinite and positive, potential energy is inifinite and negative for the bound state of a delta potential. Only their difference is well defined and negative.