L19.2 Energy eigenstates: incident and outgoing waves. Scattering amplitude

TL;DR

This video introduces the scattering problem in quantum mechanics and discusses the equations and wave functions involved.

Transcript

OK. So that's our introduction to the subject. Now, we have to get going. We have to explore how to set up this scattering problem. So equations that we need to solve. Well, what are the equations? We will have a Hamiltonian, which is p squared over 2m plus a potential v of r. Need not be yet a central potential. As usual, we will think of a wave f... Read More

Key Insights

• 🦾 The scattering problem in quantum mechanics involves solving the Hamiltonian and Schrödinger equation.
• ❓ Energy eigenstates are used to describe the scattering process.
• 🧡 Finite range potentials can have an impact on the scattering behavior.
• 👋 The scattering amplitude, f(theta, phi), plays a crucial role in understanding the directionality of the scattered waves.
• 🌥️ The solutions for the scattering problem are valid for large distances from the potential.

Questions & Answers

Q: What are the equations involved in the scattering problem in quantum mechanics?

The equations involved are the Hamiltonian, which includes the kinetic energy and potential energy, and the time-independent Schrödinger equation.

Q: How are energy eigenstates related to the scattering problem?

Energy eigenstates are the solutions to the Schrödinger equation and are used to describe the scattering process.

Q: What is the significance of finite range potentials in scattering?

Finite range potentials are commonly encountered in scattering problems, and they can affect the behavior of the scattered waves. Potentials that fall off faster are easier to work with.

Q: What is the scattering amplitude?

The scattering amplitude, represented by f(theta, phi), is a quantity that describes the scattering process in terms of how the scattered waves propagate in different directions.

Summary & Key Takeaways

• The video introduces the Hamiltonian and Schrödinger equation in the context of scattering off a potential.

• The concept of energy eigenstates and the time-independent Schrödinger equation are explained.

• The video discusses the importance of finite range potentials and how they affect the scattering process.