Susskind Quantum Mechanics Questions to answer
Use these as active-recall prompts while moving through the lecture notes.
Foundations
- In Susskind QM Lecture 1 - Systems and Experiments, what exactly is prepared by a measurement, and what is not prepared?
- Why is a single spin a complete two-dimensional system rather than a tiny arrow with hidden components? See Qubit and spin.
- What does it mean to say that a quantum state is complete but not deterministic in the classical sense? See Quantum state.
States, bases, and observables
- Given |Ψ⟩ = α|u⟩ + β|d⟩, can I compute all z-measurement probabilities and check normalization?
- Can I rewrite |u⟩ and |d⟩ in the x-basis without losing track of amplitudes versus probabilities?
- Why must observables be Hermitian? What physical role do real eigenvalues play? See Observables and eigenvalues.
- What is the difference between “the state is an eigenstate of M” and “we know the expectation value of M”?
Dynamics and uncertainty
- How does unitarity preserve distinguishability? See Quantum time evolution.
- Starting from iħ d|Ψ⟩/dt = H|Ψ⟩, can I explain why H generates time translations?
- If [L, M] = 0, can I construct the shared-eigenbasis story in words? If [L, M] ≠ 0, what fails? See Commutators and compatible observables.
- Can I derive the rough meaning of Δx Δp ≥ ħ/2 from [X, P] = iħ? See Uncertainty principle.
Composite systems and entanglement
- For two qubits, can I list the four product basis states and identify which index belongs to Alice and which to Bob? See Tensor product states.
- Given coefficients ψ_ab, can I tell whether the state factorizes?
- For the singlet-style state, what local probabilities does Alice see, and what correlations appear only after Alice and Bob compare notes? See Entanglement.
- How does the Density matrix encode a subsystem when the total state is entangled?
Particles and waves
- Why is ψ(x) a wavefunction in the position basis rather than the state itself? See Wavefunction.
- How do X and P act on ψ(x)?
- How does the usual particle Hamiltonian turn the abstract Schrödinger equation into a differential equation? See Schrödinger equation.
Harmonic oscillator
- Why does a quadratic potential appear near almost any stable equilibrium?
- How do ladder operators produce evenly spaced energy levels?
- Why is the ground state not allowed to have exactly zero position and zero momentum uncertainty? See Quantum harmonic oscillator.
Integration prompts
- Which ideas from the classical Susskind Lecture 1 - Classical Mechanics survive in quantum mechanics, and which are replaced?
- Can I explain the whole book in five nouns: state, observable, amplitude, unitary, tensor?