Скачать или смотреть 03. Schrödinger & Heisenberg Picture + Quantum Harmonic Oscillator | QFT | Dr. Jamil Aslam

September 25, 2025

Course Instructor:
Dr. Muhammad Jamil Aslam
(Professor, Department of Physics, Quaid-i-Azam University, Islamabad)

Timestamps:

Schrödinger Picture
00:00 Recap
02:58 Probability current and equation of continuity
11:28 Current corresponding to a real wave function
13:08 A way to remember the divergence theorem

Continuity Equation
14:45 Interpretation in non-relativistic QM
16:45 Interpretation in relativistic QM
18:10 How the Dirac equation is different (coming up later in the course)
19:55 Question: relationship with stationary states

Heisenberg Picture
21:18 Time-dependent operators
22:16 From Schrödinger to Heisenberg: States
24:32 Question: What does it mean for an operator to change with time?
26:54 From Schrödinger to Heisenberg: Operators
31:12 Heisenberg's equation of motion
33:15 Commutation relations of different operators
37:58 Evolution of expectation value
47:18 Summary so far
47:53 Task

Quantum Harmonic Oscillator
49:00 Problem solving in classical mechanics
49:40 The simple harmonic potential
52:30 Relating inertial properties: mass and spring constant
54:32 Solution by Algebraic Method
1:01:23 Commutation relation of â and â†
1:03:57 Writing x̂ and p̂ in terms of â and â†
1:09:07 Writing Ĥ in terms of â and â†
1:21:44 Hello, it's Pakistan
1:23:04 Eigenstates of the Hamiltonian
1:24:02 Up next: What do the raising and lowering operators do to a state?

© Lectures are uploaded here with the express consent of Dr. Muhammad Jamil Aslam.