Two interacting quantum particles: relative motion
📚 Systems of two interacting quantum particles play a major role in physics, perhaps the most important one being the hydrogen atom, made up of a proton and an electron interacting via the Coulomb potential. In this video, we learn that we can solve the mathematical problem of two quantum particles interacting via a potential that depends on their relative position by solving two simpler problems of two fictitious non-interacting particles. As such, it sets the foundation to study the hydrogen atom in quantum mechanics.
0:00 Intro
1:13 Two-particle systems
4:24 Change of variables
13:04 Hamiltonian of two interacting particles
20:58 Separable Hamiltonians
24:35 Center of mass Hamiltonian
26:02 Relative Hamiltonian
28:55 Wrap-up
⏮️ BACKGROUND
Tensor products: • Tensor product state spaces
Eigenvalues and eigenstates: • Eigenvalues and eigenstates in quantum mec...
Position representation: • Position and momentum operators acting on ...
Free particle: [COMING SOON]
Central potentials: • Central potentials in quantum mechanics
⏭️ WHAT NEXT?
Hydrogen atom: • The hydrogen atom
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Director and writer: BM
Producer and designer: MC