Lectures

Lecture. [TISE/TDSE]

Codes

Code 1(a): Finite Square Well (Transcendental Solution Eigenvalues).
Code 1(b): Finite Square Well (Eigenfunctions (DNS)).
Code 2(a): 1D Quantum Harmonic Oscillator (Shooting).
Code 2(b): 1D Morse Potential (Shooting).
Code 2(b): 1D Morse Potential (Shooting).
Code 2(c): 1D Triangular Well (Shooting).
Code 2(d): Radial Hydrogen Atom (Shooting).
Code 2(e): Radial Yukawa Potential (Shooting).
Code 2(f): Radial An-harmonic Oscillator (Shooting).
Code 2(g): Radial Morse Potential (Shooting).
Code 3: Barrier Tunneling (using Fourier Transform).

Plots

Plot 1(a): Finite Square Well (Odd Parity).
Plot 1(b): Finite Square Well (Even Parity).
Plot 1(c): Finite Square Well (Wavefunction).
Plot 2(a): Quantum Hydrogen Oscillator (Ground State).
Plot 2(b): Quantum Hydrogen Oscillator (1st Excited State).
Plot 2(c): Quantum Hydrogen Oscillator (2nd Excited State).
Plot 2(d): Quantum Hydrogen Oscillator (3rd Excited State).
Plot 2(e): Quantum Hydrogen Oscillator (4th Excited State).
Plot 2(f): Morse Oscillator (Ground State).
Plot 2(g): Morse Oscillator (1st Excited State).
Plot 2(h): Morse Oscillator (2nd Excited State).
Plot 2(i): Morse Oscillator (3rd Excited State).
Plot 2(j): Morse Oscillator (4th Excited State).
Plot 2(k): Triangular Oscillator (Ground State).
Plot 2(l): Triangular Oscillator (1st Excited State).
Plot 2(m): Triangular Oscillator (2nd Excited State).
Plot 2(n): Triangular Oscillatortamitb (3rd Excited State).
Plot 2(o): Radial Hydrogen Atom (1s).
Plot 2(p): Radial Hydrogen Atom (2s).
Plot 2(q): Radial Hydrogen Atom (2p).
Plot 2(r): Radial Hydrogen Atom (3s).
Plot 2(s): Radial Morse Oscillator (1s).
Plot 2(t): Radial Morse Oscillator (2s).
Plot 2(u): Radial Morse Oscillator (3s).
Plot 2(v): Radial Yukawa Potential (1s).
Plot 2(w): Radial Yukawa Potential (2s).
Plot 2(x): Radial Yukawa Potential (3s).
Plot 2(y): Radial Anharmonic Oscillator (1s).
Plot 2(z): Radial Anharmonic Oscillator (2s).
Plot 2(a): Radial Anharmonic Oscillator (3s).

Topics

Finding Eigenstates Solving Transcendental Equation: To find eigenvalues of the bound state particle of mass in a one dimensional potential well by solving the transcendental equation that appears as the eigenvalue condition (graphs are to be plotted for appropriate guess values, scipy root searching package may be used) and to plot the eigenfunctions.
Use of Shooting Algorithm: Shooting algorithm for solving bound state problems (solving the ode using both Euler and Numerov algorithms) : conversion to dimensionless variable, eigenvalues and eigenvectors of the ground and first excited states.
- in one dimension (for example, the Harmonic oscillator, the Morse potential, the triangular well etc.)
- the s-wave radial equation for a particle moving in a central potential, d²U(r)⁄dr² = A(r)U(r) where A(r) = 2m ⁄ ℏ² [V(r)-E]. Some examples.
  - V(r) = - e²⁄r.
  - V(r) = - e²⁄r e^-r/a .
  - V(r) = 1⁄2 kr² + 1⁄3 br³.
  - V(r) = D(e^-2αr' - e^-αr'), where r'=r-r₀⁄r.
Time Evaluation of Wave Packet:
- Time evolution of a wave packet moving in free space by the numerical solution of the time dependent Scrödinger equation.
- Solving the TDSE to study Barrier penetration and tunneling for an initially Gaussian wavepacket.
Remarks
- Read/Understand about solving TISE to obtain eigenfunctions using Direct Matrix Method. Also play with the given code for different potentials.
- Read/Understand about solving TISE to obtain eigenfunctions using Shooting Method.
Study Materials
- An Introduction to computational Physics - T.Pang.
- Scientific Computing in Python - Abhijit Kar Gupta.
- Computational Physics problem solving with Computers - Landau, Paez, Bordeianu.
- Computational Methods for physcs - Joel Franklin.
- Computational Quantum Mechanics - Joshua Izaac, Jingbo Wang.

Lectures

Codes

Plots

Topics

Remarks

Study Materials