Quantum Harmonic Oscillator: Part 2 - Wavefunction and Time Evolution | Bohaz

In this second part of our study of the quantum harmonic oscillator, we delve into wave functions and their time evolution. We'll uncover the significance of wave functions in describing a particle's position and how they evolve over time. Join us as we decipher the quantum mysteries behind definite states of energy and their interference, offering a unique perspective on the classical world.

Keywords：
1. Quantum Harmonic Oscillator
2. Wavefunction
3. Time Evolution
4. Schrödinger Equation
5. Energy Levels
6. Definite States
7. Annihilation Operator
8. Creation Operator
9. Ground State
10. Momentum Operator
11. Probability Density
12. Quantum Interference
13. Uncertainty Principle
14. Classical Physics
15. Quantum Mechanics
16. Angular Momentum
17. Spinning Particles
18. Rotation Axis
19. Quantum Spin
20. Particle Motion
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#QuantumHarmonicOscillator #Wavefunction #TimEvolution #Quantummechanics #SchrödingerEquation#EnergyLevels #oxford #christchurch #Bohaz
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Music:

Spring Flowers by Keys of Moon | https://soundcloud.com/keysofmoon
Music promoted by https://www.chosic.com/free-music/all/
Creative Commons CC BY 4.0
https://creativecommons.org/licenses/by/4.0/

Animations:

Animations are created by me using python and Manim.
https://www.manim.community/

Reference text:

The Physics of Quantum Mechanics - James Binney I David Skinner

Reference videos:
“Why is momentum operator -iℏd/dx ?”:**
https://youtu.be/arGRJpAp5f0
Method of wave function visualisation inspired by 3Blue1Brown (Manim)
Reference video: “How (and why) to raise e to the power of a matrix | DE6”
https://youtu.be/O85OWBJ2ayo
Video idea inspired by a series of year 2 quantum mechanics lectures in Oxford university physics department by James Binney.
https://youtube.com/playlist?list=PLB3CF07ACB3DBC849&si=QmvCqaRZ3VP4FKyN
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00:00 - Intro
01:23 - Finding wave functions
04:34 - Graphs of wave functions and interpretation
05:59 - Finding time evolutions of wave functions
06:51 - Time evolution of definite states of energy
08:42 - Time evolution after quantum interference between definite states of energy
11:28 - Summary and Outro