Skills

Physics 10: Quantum Physics II

14 weeks · 3 milestones

State spaces, spin, angular momentum and approximation methods. Course 10 of the Varsity Curriculum: Physics. Free sources only.

Part of: Physics · Proves for: UG

Milestone map

3 milestones

State spaces, spin and two-state systems

5 weeks (about 12 hrs/week)

Work through the first half of the 8.05 notes and videos. Then solve 8.05 problem sets 1–4, then the 2011 test timed. Self-check: MIT 8.05 past tests and final exams (2011–2013).

Proof required

Link the public repo with 8.05 problem sets 1–4, then the 2011 test timed 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

Bras, kets and operators are used consistently.
Spin results are checked with explicit matrices.
Each answer is checked a second way (a limit, a special case or a quick numerical check), and what you changed is noted.

Common mistakes

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

Powstik Guide

A public write-up of 8.05 problem sets 1–4, then the 2011 test timed, 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 10: Quantum Physics II, unit 1: State spaces, spin and two-state systems
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

Bras, kets and operators are used consistently.
Spin results are checked with explicit matrices.
Each answer is checked a second way (a limit, a special case or a quick numerical check), and what you changed is noted.
Is the physics right, not just the final number?

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

Angular momentum and approximation methods

5 weeks (about 12 hrs/week)

Work through the second half of the 8.05 notes and videos. Then solve 8.05 problem sets 5–8, then one past final timed. Self-check: MIT 8.05 past tests and final exams (2011–2013).

Proof required

Link the public repo with 8.05 problem sets 5–8, then one past final timed 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

Addition of angular momentum lists every allowed total.
Perturbation results are checked against an exact case.
Each answer is checked a second way (a limit, a special case or a quick numerical check), and what you changed is noted.

Common mistakes

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

Powstik Guide

A public write-up of 8.05 problem sets 5–8, then one past final timed, 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 10: Quantum Physics II, unit 2: Angular momentum and approximation methods
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

Addition of angular momentum lists every allowed total.
Perturbation results are checked against an exact case.
Each answer is checked a second way (a limit, a special case or a quick numerical check), and what you changed is noted.
Is the physics right, not just the final number?

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

Test perturbation theory against an exact answer

5 weeks (about 12 hrs/week)

Make a notebook that compares first- and second-order perturbation theory with exact numerical energies for an anharmonic oscillator. Add a small x⁴ term, compute the corrections by hand, diagonalise the matrix numerically, and find the coupling where second order is off by more than 1 %.

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

Hand corrections match the numbers for small coupling.
The coupling where second order is off by more than 1 % is found, and why the series fails is explained.
The matrix is big enough that the results no longer change.

Common mistakes

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

Powstik Guide

A notebook that compares first- and second-order perturbation theory with exact numerical energies for an anharmonic oscillator, in a public repo.

Steps

Write down what you expect before you start.
Add a small x⁴ term, compute the corrections by hand, diagonalise the matrix numerically, and find the coupling where second order is off by more than 1 %.
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 10: Quantum Physics II — Test perturbation theory against an exact answer
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

Hand corrections match the numbers for small coupling.
The coupling where second order is off by more than 1 % is found, and why the series fails is explained.
The matrix is big enough that the results no longer change.
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 10: Quantum Physics II →

Related outcomes

Milestone map

3 milestones

State spaces, spin and two-state systems

5 weeks (about 12 hrs/week)

Work through the first half of the 8.05 notes and videos. Then solve 8.05 problem sets 1–4, then the 2011 test timed. Self-check: MIT 8.05 past tests and final exams (2011–2013).

Proof required

What gets checked

Bras, kets and operators are used consistently.
Spin results are checked with explicit matrices.
Each answer is checked a second way (a limit, a special case or a quick numerical check), and what you changed is noted.

Common mistakes

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

Powstik Guide

A public write-up of 8.05 problem sets 1–4, then the 2011 test timed, 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 10: Quantum Physics II, unit 1: State spaces, spin and two-state systems
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

Bras, kets and operators are used consistently.
Spin results are checked with explicit matrices.
Each answer is checked a second way (a limit, a special case or a quick numerical check), and what you changed is noted.
Is the physics right, not just the final number?

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

Angular momentum and approximation methods

5 weeks (about 12 hrs/week)

Work through the second half of the 8.05 notes and videos. Then solve 8.05 problem sets 5–8, then one past final timed. Self-check: MIT 8.05 past tests and final exams (2011–2013).

Proof required

What gets checked

Addition of angular momentum lists every allowed total.
Perturbation results are checked against an exact case.
Each answer is checked a second way (a limit, a special case or a quick numerical check), and what you changed is noted.

Common mistakes

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

Powstik Guide

A public write-up of 8.05 problem sets 5–8, then one past final timed, 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 10: Quantum Physics II, unit 2: Angular momentum and approximation methods
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

Addition of angular momentum lists every allowed total.
Perturbation results are checked against an exact case.
Each answer is checked a second way (a limit, a special case or a quick numerical check), and what you changed is noted.
Is the physics right, not just the final number?

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

Test perturbation theory against an exact answer

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

Hand corrections match the numbers for small coupling.
The coupling where second order is off by more than 1 % is found, and why the series fails is explained.
The matrix is big enough that the results no longer change.

Common mistakes

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

Powstik Guide

A notebook that compares first- and second-order perturbation theory with exact numerical energies for an anharmonic oscillator, in a public repo.

Steps

Write down what you expect before you start.
Add a small x⁴ term, compute the corrections by hand, diagonalise the matrix numerically, and find the coupling where second order is off by more than 1 %.
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 10: Quantum Physics II — Test perturbation theory against an exact answer
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

Hand corrections match the numbers for small coupling.
The coupling where second order is off by more than 1 % is found, and why the series fails is explained.
The matrix is big enough that the results no longer change.
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.