Nine formulations of nonrelativistic quantum mechanics are reviewed. These are the wavefunction, matrix, path integral, phase space, density matrix, second quantization, variational, pilot wave, and Hamilton–Jacobi formulations. Also mentioned are the many-worlds and transactional interpretations. The various formulations differ dramatically in mathematical and conceptual overview, yet each one makes identical predictions for all experimental results.

This paper lists fifteen commonly held misconceptions concerning quantum mechanics, such as "Energy eigenstates are the only allowed states" and "The wavefunction is dimensionless". A few suggestions are offered to help combat these misconceptions in teaching.

What is the qualitative character of entropy? Several examples from statistical mechanics (including liquid crystal reentrant phases, two different lattice gas models, and the game of poker) demonstrate facets of this difficult question and point toward an answer. The common answer of “entropy as disorder” is regarded here as inadequate. An alternative but equally problematic analogy is “entropy as freedom.” Neither simile is perfect, but if both are used cautiously and not too literally, then the combination provides considerable insight.

A particle of mass M moves in an infinite square well of width L (the "particle in a box"). Classically, the motion has period L 2M/E, which depends upon the initial condition through the energy E. Quantum mechanically, any wavefunction repeats exactly with period 4M L 2 /πh, independent of the initial condition. Given this qualitative difference, how can the classical motion possibly be the limit of the quantal time development? The resolution of this paradox involves the difference between the exact revival (recurrence) of the wavefunction and the approximate periodicity of expectation values such as x(t). (The latter may recur an odd integral number of times before the full wavefunction recurs.) The period of the expectation values does depend on the initial condition and can possess the expected classical limit.

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