- #61
gracy
- 2,486
- 83
Yup. First chapter is " The wave function" .BvU said:
Planar wave solution to zero potential Schrödinger equation
- Thread starter Schwarzschild90
- Start date
Click For Summary
SUMMARY
The discussion centers on the planar wave solution to the zero potential Schrödinger equation, specifically the wave function represented as ##\psi(x, t) = e^{(ikx - i\omega t)}## with a constant potential ##V(x) = 0##. Participants analyze the implications of this wave function, including its time and spatial derivatives, and the resulting dispersion relation ##\omega(k) = \frac{\hbar}{2m} k^2##. The conversation also touches on the significance of parity in distinguishing eigenstates of the Hamiltonian, emphasizing the need for additional observables to resolve degeneracies in energy eigenvalues.
PREREQUISITES- Understanding of the Schrödinger equation and its solutions
- Familiarity with complex exponentials and their applications in quantum mechanics
- Knowledge of eigenstates and eigenvalues in quantum systems
- Basic concepts of wave functions and their properties in quantum mechanics
- Study the derivation and implications of the dispersion relation ##\omega(k) = \frac{\hbar}{2m} k^2##
- Explore the concept of parity in quantum mechanics and its role in distinguishing eigenstates
- Investigate the time-dependent Schrödinger equation and its solutions for various potentials
- Learn about the relationship between momentum eigenstates and parity eigenstates in quantum systems
Quantum mechanics students, physicists, and researchers interested in wave functions, eigenstate analysis, and the mathematical foundations of quantum theory.
Similar threads
- · Replies 1 ·
- · Replies 6 ·
- · Replies 5 ·
- · Replies 9 ·
- · Replies 6 ·
- · Replies 8 ·
- · Replies 4 ·