Solving Shrodinger Eqn for Constrained System: Negative Energy Levels?

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Discussion Overview

The discussion revolves around the interpretation of negative energy levels in the context of solving the Schrödinger equation for constrained systems. Participants explore the implications of these negative energy levels, particularly in relation to binding energy and the existence of bound states.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested

Main Points Raised

  • One participant suggests that negative energy levels indicate energy that is "released" and questions how a system can exist in such a state.
  • Another participant counters that negative energy levels represent a negative energy offset and asserts that the ground state is always present, emphasizing that the reference point for energy can be redefined without affecting the forces involved.
  • A participant raises a question about the relationship between energy levels and binding energy, seeking clarification on the source of binding energy if no energy is released when a bound system is formed.
  • Another participant explains that it is conventional to set bound states as negative in atomic-like potentials, indicating that adding binding energy can excite an electron to a state where it is free from the nucleus.

Areas of Agreement / Disagreement

Participants express differing views on the interpretation of negative energy levels and their implications for binding energy, indicating that multiple competing perspectives remain in the discussion.

Contextual Notes

There are unresolved assumptions regarding the definitions of energy levels and binding energy, as well as the implications of negative energy states in quantum systems.

sudabe
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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.
 
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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.
 
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?
 
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.
 

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