Quantum Mechanics True/False Quiz

Light frequency and wavelength have an inverse relationship; as frequency increases, wavelength decreases.
Photons vary in energy, described by the equation E = hν, where ν represents the frequency; thus, not all photons possess the same energy.

The ground state energy level for a particle in a box is n=1; n=0 indicates no particle in the box.
Maximum probability density in PIB stationary states is not at the center of the box, which actually has zero probability density.
For the n=1 state, the probability of finding the particle in the left third of the box does not equal the probability in the middle third due to lack of symmetry in this state.
PIB energy levels are not equally spaced; energy spacing increases with n according to the formula ΔE = (2nπh²)/(8ma²).

Probability density is always positive; it cannot be negative, even for non-real wavefunctions.
For quantum states, the wavefunction Ψ(x, t) does not always separate into independent functions of x and t; this only occurs if the Hamiltonian is time-independent.

The product of a number and its complex conjugate is always a real number.
The measurement of an observable leads to an eigenvalue, even if the wavefunction is not an eigenfunction of the corresponding operator.
A linear combination of two solutions to the time-independent Schrödinger equation is not guaranteed to be a solution unless both solutions share the same eigenvalues.
If a function is an eigenfunction of the operator Â with eigenvalue a, it remains an eigenfunction of the operator Â² but with eigenvalue a².
Hermitian operators are defined as equal to their complex conjugate transpose, but this does not imply that they are real.
Commuting eigenfunctions do not necessarily share the same eigenfunctions; they can possess a mutual set of eigenfunctions.
A wavefunction that is simultaneously an eigenfunction of two operators will also be an eigenfunction of the product of those operators.