# Double delta potential -- Degeneracy of bound states in one dimension?

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• LagrangeEuler
In summary, the Double Delta Potential is a mathematical model used to describe the behavior of particles in one-dimensional systems. This potential exhibits a unique property called degeneracy, where multiple energy levels of the particle can have the same energy. This phenomenon is crucial in understanding the behavior of bound states and can have significant implications in various fields of physics, such as quantum mechanics and solid-state physics.
LagrangeEuler
I have a question from the youtube lecture

That part starts after 42 minutes and 47 seconds.
Balakrishnan said that if delta barriers are very distant (largely separated) then we have degeneracy. I do not understand how this is possible when in 1d problems there is no degeneracy for bond states.

If I have two identical delta functions very far away and one particle, to a very good approximation it is either in potential #1 or in potential #2. They have the same energy (to an even better approximation) so the system is degenerate.

Last edited:
vanhees71
So if I understand you well it is practical like two separate systems? Because of how to comment on this in the context of that in the one-dimensional problems there is no degeneration in the case of bond states.

## 1. What is a double delta potential?

A double delta potential is a type of potential energy function used in quantum mechanics to describe the behavior of particles in one dimension. It consists of two delta functions, which represent two point-like interactions that can affect the motion of a particle.

## 2. What is degeneracy in quantum mechanics?

Degeneracy refers to the phenomenon in which multiple quantum states have the same energy level. This means that the system can exist in any of these states without any change in energy. In the case of bound states in a double delta potential, degeneracy occurs when multiple energy levels have the same value.

## 3. How is the degeneracy of bound states in one dimension affected by a double delta potential?

The degeneracy of bound states in one dimension is affected by the strength and position of the two delta functions in the double delta potential. If the two delta functions are identical, the energy levels will be equally spaced and have the same degeneracy. However, if the two delta functions are different, the energy levels may have different degeneracies.

## 4. What is the significance of degeneracy in quantum mechanics?

Degeneracy plays a crucial role in determining the properties and behavior of quantum systems. It can affect the stability and symmetry of a system, as well as the probability of finding a particle in a particular state. In the case of bound states in a double delta potential, degeneracy can affect the energy levels and the likelihood of a particle being in a certain energy state.

## 5. How is the degeneracy of bound states in one dimension calculated for a double delta potential?

The degeneracy of bound states in one dimension for a double delta potential can be calculated using the Schrödinger equation and the boundary conditions at the delta functions. The solutions to the equation will yield the energy levels and corresponding wave functions, from which the degeneracy can be determined. Alternatively, numerical methods can also be used to calculate the degeneracy.

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