True or false? (a) The state function is always equal to a function of time multiplied by a function of the coordinates. (b) In both classical and quantum mechanics, knowledge of the present state of an isolated system allows its future state to be calculated. (c) The state function is always an eigenfunction of the Hamiltonian. (d) Every linear combination of eigenfunctions of the Hamiltonian is an eigenfunction of the Hamiltonian operator. (e) If the state function is not an eigenfunction of the operator Â, then a measurement of the property A might give a value that is not one of the eigenvalues of Â. (f) The probability density is independent of time for a stationary state. (g) If two Hermitian operators do not commute, then they cannot possess any common eigenfunctions. (h) If two Hermitian operators commute, then every eigenfunction of one must be an eigenfunction of the other. (i) Two linearly independent eigenfunctions of the same Hermitian operator are always orthogonal to each other. (j) If the operator corresponds to a physical property of a quantum-mechanical system, the state function ( must be an eigenfunction of. (k) Every linear combination of solutions of the time-dependent Schrödinger equation is a solution of this equation. (l) The normalized state function ( is dimensionless (that is, has no units). (m) All eigenfunctions of Hermitian operators must be real functions. (n) The quantities

are numbers. (o) When ( is an eigenfunction of with eigenvalue bk, we are certain to observe the value bk when the property B is measured. (p) The relation

is valid only when f and g are eigenfunctions of the Hermitian operator . (q) The time-dependent Schrödinger equation is more fundamental than the time-independent Schrödinger equation. (r) For all states, (() / ( is equal to the energy E of the state.

Transcribed Image Text:

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