Solving Shrodinger Eqn for Constrained System: Negative Energy Levels?

[sudabe]

If we solve the shrodinger equation for a constrained system we will find some negative energy levels.The nagative sign shows that this energy is released and no longer exist in the system.
Then how we can say the system is in this level with this ENERGY?
are we talking about something that doesn't exist?
I appreciate if you help.

 

[per.sundqvist]

No, its just a negative energy offset that makes your energy negative, the ground state is always existing, and not "released". You could always add a constant to a potential energy, since it won't affect forces f=d(V(x)-E0)/dx=dV/dx. It will redefine your reference point of energy only.

 

[sudabe]

then what is the relation between the energy levels and binding energy?
If no energy will be released(when a bound system is formed) then where does the binding energy come from?

 

[per.sundqvist]

the convention s normal to set all bound states negative in atomic like potentials, for example V=-1/r, so if you add the binding energy (by light) you excite the electron up to V=0, meaning its free from the nucleus.