Estimate of ground state energy for the Yukawa potential

I
Thread starter L_landau
Start date Nov 11, 2018
Tags

Energy Estimate Ground Ground state Ground state energy Potential Quantum State Yukawa Yukawa potential

In summary, the Yukawa potential is a mathematical model used to describe the interaction between particles, commonly used in quantum mechanics. The ground state energy, which is the lowest possible energy of a system, is related to the Yukawa potential and is calculated using the Schrödinger equation. Factors such as the strength of the potential, distance between particles, and mass can affect the estimate of ground state energy. The estimate for the Yukawa potential is typically lower than other potential models due to its consideration of the finite range of interaction. Real-world applications of estimating the ground state energy for the Yukawa potential include nuclear and particle physics, as well as the development of technologies and studying properties of atoms and molecules.

Nov 11, 2018

L_landau

I’ve seen the uncertainty principle used to calculate the ground state energy for things like hydrogen and the harmonic oscillator, but can this be done for the Yukawa potential where you have an exponential?

Physics news on Phys.org

Nov 17, 2018

PeterDonis

Mentor

Insights Author

L_landau said:

I’ve seen the uncertainty principle used to calculate the ground state energy for things like hydrogen and the harmonic oscillator

Can you give a specific reference?

1. What is the Yukawa potential and how is it related to ground state energy?

The Yukawa potential is a mathematical model used to describe the interaction between two particles. It is commonly used in quantum mechanics to study the behavior of subatomic particles. The ground state energy is the lowest possible energy that a system can have, and it is related to the Yukawa potential as it determines the stability and behavior of the particles in the system.

2. How is the ground state energy for the Yukawa potential calculated?

The ground state energy for the Yukawa potential is calculated using the Schrödinger equation, which is a fundamental equation in quantum mechanics that describes the behavior of a quantum system. The equation is solved using mathematical techniques such as perturbation theory or numerical methods to obtain an estimate of the ground state energy.

3. What are the factors that affect the estimate of ground state energy for the Yukawa potential?

There are several factors that can affect the estimate of ground state energy for the Yukawa potential. These include the strength of the potential, the distance between the particles, and the mass of the particles. In addition, the accuracy of the mathematical methods used to solve the Schrödinger equation and any approximations made can also impact the estimate.

4. How does the estimate of ground state energy for the Yukawa potential compare to other potential models?

The estimate of ground state energy for the Yukawa potential is typically lower than that of other potential models, such as the Coulomb potential or the harmonic oscillator potential. This is because the Yukawa potential takes into account the finite range of the interaction between particles, whereas other models assume an infinite range.

5. What are the real-world applications of estimating the ground state energy for the Yukawa potential?

Estimating the ground state energy for the Yukawa potential has many real-world applications, particularly in the fields of nuclear physics and particle physics. It is used to understand the behavior of subatomic particles and their interactions, as well as in the development of new technologies such as particle accelerators and nuclear reactors. It is also relevant in studying the properties of atoms and molecules in chemistry and materials science.