Practice Midterm Flashcards
A valid wavefunction must be single-valued and not go to infinity
True
(must be single-valued and not go to infinity)
A valid wavefunction must be an eigenfunction of the Hamiltonian
False
(A valid wavefunction does not have to be an eigenfunction of the Hamiltonian)
The eigenvalues of a Hermitian operator must be real numbers
True
(MUST BE REAL #’S)
The eigenfunctions of a nondegenerate Hermitian Operator must be orthogonal
True
(Hermitian = orthogonal)
Nondegenerate
quantum states that have unique energy levels, meaning that no two states share the same energy value
The most probable location of a particle in a box is always L/2
False
(depends on energy & quantum number)
For a particle in a box in a stationary state <p>=0
True
(momentum cancels itself out)
If [A,B] = 0, then A and B must have the same eigenfunctions
False.
(If they commute, they can share a common set, but not necessarily having same e-functions)
Any valid wavefunction can be constructed using the eigenfunctions of a Hermitian operator.
True.
(Hermitian is good, so yes)
A small particle will behave classically when it has low kinetic energy.
False.
(Reverse. remember the amount of oscillations and nodes contributing to a straiter line)
The energy of a rigid rotor depends on both quantum numbers l and m.
False
(depends on l more than m)
Kinetic Energy equals
(3/2)kB *T
Kinetic Energy equals
(1/2)mv^2
mass of electron
9.11 x 10^-31
If particles travel at the same energy, they must have the same de Broglie wavelength.
False
(need to have the same mass)
The expectation value <x> gives the most probable location for the particle in a box</x>
False
(average position not most probable)
A valid wavefunction must satisfy integral |Psi(x)|^2 = 1
True
(needs to satisfy the normalization condition, total probability of finding the particle somewhere in space is 1)
The Heisenburg representation of a wavefunction is a matrix.
False (they are state vectors)
The eigenfunctions of the Hamiltonian are the only possible quantum states of the system.
False
(they represent stationary states, not superpositions)
A well-behaved wavefunction cannot go to infinity on the interval where it is defined.
True
(A well-behaved wavefunction must be finite - not go to infinity)
A superposition state is also called a nonstationary state.
True.
(unlike a single energy eigenstate, a superposition of multiple eigenstates generally results in time-dependent behavior - leading to a nonstationary state)
The nondegenerate eigenstates of a Hermitian operator must be orthogonal (by default)
.
True.
(Follows properties of Hermitian operators, guarantee the eigenstates corresponding to different eigenvalues are orthogonal)
The eigenfunctions of the rigid rotor Hamiltonian are non degenerate.
False
(They exhibit degeneracy. E-values are nondegenerate for l, but the E-Functions are degenerate)
If two operators commute, there will be an uncertainty relation between their observables.
False
(There is no uncertainty. Heisenburg Uncertainty principle applies to non-commuting observables).
