Solving Shrodinger Eqn for Constrained System: Negative Energy Levels?

In summary, solving the Schrodinger equation for a constrained system can result in finding negative energy levels, signifying that this energy is released and no longer exists in the system. However, this does not mean that the system does not exist in this level with the negative energy. The negative energy offset only redefines the reference point of energy and does not affect the existence of the ground state. In atomic-like potentials, it is conventionally normal to set all bound states as negative, such as in the case of V=-1/r. Adding binding energy through light can excite the electron and free it from the nucleus, resulting in the electron being at V=0.
  • #1
sudabe
8
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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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  • #2
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.
 
  • #3
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?
 
  • #4
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.
 

1. What is the Schrodinger equation for a constrained system with negative energy levels?

The Schrodinger equation is a fundamental equation in quantum mechanics that describes the time evolution of a quantum system. For a constrained system with negative energy levels, the Schrodinger equation takes the form of a second-order partial differential equation, with the energy levels being represented by the solutions to the equation.

2. How do you solve the Schrodinger equation for a constrained system with negative energy levels?

Solving the Schrodinger equation for a constrained system with negative energy levels involves using mathematical methods such as separation of variables, perturbation theory, and variational methods. These methods allow for the determination of the energy levels and corresponding wavefunctions for the system.

3. What does it mean for a system to have negative energy levels?

Negative energy levels in a quantum system refer to energy states that have a lower energy than the ground state or the lowest possible energy state. In some cases, negative energy levels may arise due to the presence of external constraints or interactions within the system.

4. How do negative energy levels affect the behavior of a quantum system?

The presence of negative energy levels can significantly impact the behavior and properties of a quantum system. For example, negative energy levels can lead to the emergence of exotic phenomena such as vacuum decay and the Casimir effect. They can also influence the stability and dynamics of the system, as well as the possibility of energy absorption and emission processes.

5. Are negative energy levels experimentally observed in real-world systems?

While negative energy levels are a theoretical concept in quantum mechanics, there are some experimental observations that can be attributed to their existence. For example, the Lamb shift in atomic spectra and the anomalous magnetic moment of the electron are both considered to be consequences of negative energy levels. However, further research and experimentation are still needed to fully understand and confirm the existence of negative energy levels in real-world systems.

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