Bound state of the delta function potential.

In summary, the concept of a bound state with negative energy in the case of a delta function potential means that the potential function is identically zero except at its peak. This results in a system with a negative kinetic energy, but the zero point of potential energy is arbitrary and does not hold physical significance. In classical physics, potentials work the same way with kinetic energy being infinite and positive, and potential energy being infinite and negative for the bound state of a delta potential.
  • #1
siddharth5129
94
3
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 ?
 
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  • #2
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.
 
  • #3
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.
 

1. What is a bound state of the delta function potential?

A bound state of the delta function potential is a quantum mechanical state in which a particle is confined to a specific region of space due to the presence of a delta function potential. This potential is a very strong potential that acts as an infinitely high barrier, preventing the particle from escaping.

2. How is the bound state of the delta function potential different from other bound states?

The bound state of the delta function potential is different from other bound states because it is an idealized potential that does not exist in physical systems. It is used as a theoretical model to understand the behavior of particles in confined spaces.

3. What is the significance of studying the bound state of the delta function potential?

Studying the bound state of the delta function potential allows us to gain a better understanding of quantum mechanics and how particles behave in confined spaces. It also has important applications in fields such as quantum computing and nano-scale devices.

4. How is the bound state of the delta function potential calculated?

The bound state of the delta function potential is calculated using mathematical techniques such as the Schrodinger equation and the Dirac delta function. These equations allow us to determine the energy levels and wavefunctions of the particle in the potential.

5. Can the bound state of the delta function potential be observed experimentally?

No, the bound state of the delta function potential cannot be observed experimentally as it is an idealized model. However, the principles and mathematical techniques used to study this potential can be applied to real-world systems to make predictions and understand their behavior.

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