Undergraduate Problem Map

This route is for a first serious pass through quantum mechanics. It emphasizes reliable setup, not speed.

Route

Stage	Problem Family	Canonical Page	Outcome
1	Prerequisite check	Self-Diagnostic Quiz	identify review needs
2	Problem workflow	How to Solve Problems	state system, Hilbert space, Hamiltonian, observable
3	Formalism basics	Exercises and Problems	basis changes, probabilities, expectation values
4	Wave mechanics	Exercise Sets	normalization, boundary conditions, spectra
5	Scattering and current	Scattering Examples	reflection and transmission as flux ratios
6	Matrix and spin systems	Spin Examples and Matrix-Mechanics Examples	two-level systems and measurement axes
7	Composite systems	Tensor Product Exercises	product bases and local operators
8	Density matrices	Partial Trace Exercises	reduced states and local predictions

Representative Problem IDs

ID	Prompt Type	Skills	Solution Status
QM-PROB-U101	Normalize a finite vector and a wavefunction	normalization, units	full solution available through diagnostic pages
QM-PROB-U201	Compute Born-rule probabilities in two bases	basis change, relative phase	full solution in Core Formalism
QM-PROB-U301	Derive infinite-well quantization	boundary conditions, eigenvalues	exercise set
QM-PROB-U302	Match a delta-potential derivative jump	distributional potential, matching	exercise set
QM-PROB-U401	Compute reflection and transmission for a step	current, flux ratios	canonical scattering route
QM-PROB-U501	Factor or diagnose a two-qubit product state	tensor products, rank-one coefficient matrix	full solution in composite exercises

Minimum Mastery Checks

Before moving to graduate problems, a reader should be able to:

• normalize a state in the correct measure;
• identify the observable being measured;
• compute probabilities and expectation values;
• solve a basic boundary-value eigenproblem;
• use probability current for one-dimensional scattering;
• diagonalize a $2\times2$ Hermitian matrix;
• write a two-qubit state in a fixed product basis;
• explain the difference between a superposition and a mixture.

References

• D. J. Griffiths and D. F. Schroeter, Introduction to Quantum Mechanics, 3rd ed., Cambridge University Press, 2018.
• R. Shankar, Principles of Quantum Mechanics, 2nd ed., Springer, 1994.
• D. A. B. Miller, Quantum Mechanics for Scientists and Engineers, Cambridge University Press, 2008.

Exercises

1. Which stage should a reader revisit if they can solve the Schrödinger equation in a box but cannot explain what measurement produces the answer?

Solution

Return to the formalism basics and problem workflow stages. The issue is interpretation of states, observables, and probabilities, not the differential equation itself.