Skills

Physics 9: Quantum Physics I

14 weeks · 3 milestones

Wave functions, the Schrödinger equation, operators and simple systems. Course 9 of the Varsity Curriculum: Physics. Free sources only.

Part of: Physics · Proves for: UG

Milestone map

3 milestones

Wave mechanics in one dimension

5 weeks (about 12 hrs/week)

Watch the 8.04 (2016) lectures on wave functions, the Schrödinger equation, wells and barriers. Then solve the 8.04 (2013) problem sets on one-dimensional systems. Self-check: MIT 8.04 (Spring 2013) problem sets with solutions.

Proof required

Link the public repo with the 8.04 (2013) problem sets on one-dimensional systems written up (a typeset PDF, LaTeX source or notebook), and show the self-check: which answers matched and how you fixed the ones that did not.

What gets checked

Wave functions are normalised.
Boundary conditions fix every energy level.
Each set is marked against its solutions.

Common mistakes

Answers copied from the key with no working.
Wrong units or missing signs.

Powstik Guide

A public write-up of the 8.04 (2013) problem sets on one-dimensional systems, with the self-check shown.

Steps

Study the linked course and chapters.
Solve the problems on your own first.
Check them against the self-check and rework the misses.
Typeset the write-up (LaTeX or a notebook) in a public repo.
Ask someone who knows physics to check it.

Template

README
Physics 9: Quantum Physics I, unit 1: Wave mechanics in one dimension
Problems:
Self-check result (matched / reworked):
What I got wrong first and why:

What gets sent back

No working shown.
The self-check result is missing.

Resources

Foundationstart here

Depthgo deeper

What a verifier looks for

Wave functions are normalised.
Boundary conditions fix every energy level.
Each set is marked against its solutions.
Is the physics right, not just the final number?

You'll sign in first, then come straight back here.

Operators, the oscillator and hydrogen

5 weeks (about 12 hrs/week)

Watch the 8.04 (2016) lectures on operators, the harmonic oscillator and the hydrogen atom. Then solve the 8.04 (2013) problem sets on operators and three dimensions. Self-check: MIT 8.04 (Spring 2013) problem sets with solutions.

Proof required

Link the public repo with the 8.04 (2013) problem sets on operators and three dimensions written up (a typeset PDF, LaTeX source or notebook), and show the self-check: which answers matched and how you fixed the ones that did not.

What gets checked

Commutators are worked out, not assumed.
Ladder operators are used correctly.
Each set is marked against its solutions.

Common mistakes

Answers copied from the key with no working.
Wrong units or missing signs.

Powstik Guide

A public write-up of the 8.04 (2013) problem sets on operators and three dimensions, with the self-check shown.

Steps

Study the linked course and chapters.
Solve the problems on your own first.
Check them against the self-check and rework the misses.
Typeset the write-up (LaTeX or a notebook) in a public repo.
Ask someone who knows physics to check it.

Template

README
Physics 9: Quantum Physics I, unit 2: Operators, the oscillator and hydrogen
Problems:
Self-check result (matched / reworked):
What I got wrong first and why:

What gets sent back

No working shown.
The self-check result is missing.

Resources

Foundationstart here

Depthgo deeper

What a verifier looks for

Commutators are worked out, not assumed.
Ladder operators are used correctly.
Each set is marked against its solutions.
Is the physics right, not just the final number?

You'll sign in first, then come straight back here.

Solve the Schrödinger equation numerically

5 weeks (about 12 hrs/week)

Make a notebook that finds the energy levels of a finite well and a harmonic oscillator by finite differences. Build the Hamiltonian as a matrix, find its eigenvalues, and compare them with the exact oscillator levels and the finite well's levels from its transcendental equation, as the grid gets finer.

Proof required

Link the public repo with the notebook, the result with its uncertainty, and a README that says what you did and what limits the result.

What gets checked

The error falls about as (grid step)², and the measured rate is shown.
Oscillator levels match (n + ½)ħω.
Wave functions are normalised and plotted.

Common mistakes

A result with no uncertainty.
Code or data that cannot be rerun from the repo.

Powstik Guide

A notebook that finds the energy levels of a finite well and a harmonic oscillator by finite differences, in a public repo.

Steps

Write down what you expect before you start.
Build the Hamiltonian as a matrix, find its eigenvalues, and compare them with the exact oscillator levels and the finite well's levels from its transcendental equation, as the grid gets finer.
Work out the uncertainty from your own data.
Compare with the accepted value and explain any gap.
Write the README and ask someone who knows physics to check it.

Template

README
Physics 9: Quantum Physics I — Solve the Schrödinger equation numerically
What I expected:
Method:
Result (value ± uncertainty):
Accepted value and comparison:
What limits the result:

What gets sent back

No uncertainty, or one that is guessed.
Code that does not run.

Resources

Foundationstart here

What a verifier looks for

The error falls about as (grid step)², and the measured rate is shown.
Oscillator levels match (n + ½)ħω.
Wave functions are normalised and plotted.
The uncertainty is worked out from the data or runs (spread of repeats, instrument limits, fit errors or a range of inputs), not guessed, and it is shown on the result.
Is the physics right, and could someone rerun it from the repo?

You'll sign in first, then come straight back here.

Part of

Physics 9: Quantum Physics I →

Related outcomes

Milestone map

3 milestones

Wave mechanics in one dimension

5 weeks (about 12 hrs/week)

Proof required

What gets checked

Wave functions are normalised.
Boundary conditions fix every energy level.
Each set is marked against its solutions.

Common mistakes

Answers copied from the key with no working.
Wrong units or missing signs.

Powstik Guide

A public write-up of the 8.04 (2013) problem sets on one-dimensional systems, with the self-check shown.

Steps

Study the linked course and chapters.
Solve the problems on your own first.
Check them against the self-check and rework the misses.
Typeset the write-up (LaTeX or a notebook) in a public repo.
Ask someone who knows physics to check it.

Template

README
Physics 9: Quantum Physics I, unit 1: Wave mechanics in one dimension
Problems:
Self-check result (matched / reworked):
What I got wrong first and why:

What gets sent back

No working shown.
The self-check result is missing.

Resources

Foundationstart here

Depthgo deeper

What a verifier looks for

Wave functions are normalised.
Boundary conditions fix every energy level.
Each set is marked against its solutions.
Is the physics right, not just the final number?

You'll sign in first, then come straight back here.

Operators, the oscillator and hydrogen

5 weeks (about 12 hrs/week)

Proof required

What gets checked

Commutators are worked out, not assumed.
Ladder operators are used correctly.
Each set is marked against its solutions.

Common mistakes

Answers copied from the key with no working.
Wrong units or missing signs.

Powstik Guide

A public write-up of the 8.04 (2013) problem sets on operators and three dimensions, with the self-check shown.

Steps

Study the linked course and chapters.
Solve the problems on your own first.
Check them against the self-check and rework the misses.
Typeset the write-up (LaTeX or a notebook) in a public repo.
Ask someone who knows physics to check it.

Template

README
Physics 9: Quantum Physics I, unit 2: Operators, the oscillator and hydrogen
Problems:
Self-check result (matched / reworked):
What I got wrong first and why:

What gets sent back

No working shown.
The self-check result is missing.

Resources

Foundationstart here

Depthgo deeper

What a verifier looks for

Commutators are worked out, not assumed.
Ladder operators are used correctly.
Each set is marked against its solutions.
Is the physics right, not just the final number?

You'll sign in first, then come straight back here.

Solve the Schrödinger equation numerically

5 weeks (about 12 hrs/week)

Proof required

Link the public repo with the notebook, the result with its uncertainty, and a README that says what you did and what limits the result.

What gets checked

The error falls about as (grid step)², and the measured rate is shown.
Oscillator levels match (n + ½)ħω.
Wave functions are normalised and plotted.

Common mistakes

A result with no uncertainty.
Code or data that cannot be rerun from the repo.

Powstik Guide

A notebook that finds the energy levels of a finite well and a harmonic oscillator by finite differences, in a public repo.

Steps

Write down what you expect before you start.
Build the Hamiltonian as a matrix, find its eigenvalues, and compare them with the exact oscillator levels and the finite well's levels from its transcendental equation, as the grid gets finer.
Work out the uncertainty from your own data.
Compare with the accepted value and explain any gap.
Write the README and ask someone who knows physics to check it.

Template

README
Physics 9: Quantum Physics I — Solve the Schrödinger equation numerically
What I expected:
Method:
Result (value ± uncertainty):
Accepted value and comparison:
What limits the result:

What gets sent back

No uncertainty, or one that is guessed.
Code that does not run.

Resources

Foundationstart here

What a verifier looks for

The error falls about as (grid step)², and the measured rate is shown.
Oscillator levels match (n + ½)ħω.
Wave functions are normalised and plotted.
The uncertainty is worked out from the data or runs (spread of repeats, instrument limits, fit errors or a range of inputs), not guessed, and it is shown on the result.
Is the physics right, and could someone rerun it from the repo?

You'll sign in first, then come straight back here.