Physical Chemistry Exam#1 T/F

question

If a wave function is simultaneously the eigenfunction of two operators, then that wave function will be an eigenfunction of the product of those operators
answer

True
question

Planck’s constant may be derived from a measurement of energy density as a function of frequency of the light emitted by a blackbody
answer

True
question

The Rydberg constant may be determined from a measurement of the frequencies in the atomic hydrogen emission spectrum
answer

True
question

According to the de Broglie picture of matter waves, heavier particles have longer wavelengths than lighter particles, for a specified velocity
answer

False
question

The displacement function in the solution to the classical wave equation for a vibrating string, Z(x,t) was written as a product z(x,t)=psi(x)E(t). In this product, psi describes the shape of the string at its maximum displacement
answer

True
question

In the particle in a box problem where the PE goes to infinity at the ends of the box, the particle is at rest when it is in the lowest-energy state
answer

False
question

Three will be no degenerate solutions to the Schrodinger eon for a particle in a 3-D box which has only two sides with equal lengths
answer

False
question

A wave fan that is not normalized may be a valid solution to the Schrodinger eon
answer

True
question

The “correspondence principle” states that quantum mechanical results agree with classical mechanical results in the limit of large quantum numbers
answer

True
question

The probability density psi*psi may be real or complex
answer

False
question

The uncertainty in the position of a particle in a box has its max when the quantum number n =1
answer

False
question

All hermitian operators are real
answer

False
question

If the momentum of an electron can be measured to any precision then the electron is a free particle
answer

True
question

The time-d schrodinger eon is an eigenvalue problem in which the eigenvalue is the energy of the stationary state
answer

True
question

If [A,B]=0 then the fcn that is an eigenfunction of A must be that of B
answer

False
question

Acceptable units for 1-D wave fcn would be m^-1
answer

False
question

If 2 operators, A and B, commute, then there exists an uncertainty relationship between their corresponding observable variables, a and b
answer

False
question

If A is a linear operator then A[f(x)+g(x)]=Af(x)+Ag(x)
answer

True
question

A particle satisfying the time-i eqn must have a total energy that is independent of its position
answer

True
question

The wavelike character of electrons is demonstrated by the photoelectric effect
answer

False
question

If two operators commute, then they must share a set of eigenfunctions
answer

True
question

A complete orthonormal set of wave functions is sufficient to describe any arbitrary state of a system, even if the state is not an eigenstate of the hamiltonian operator
answer

True
question

No two eigenfunctions of the same operator can have the same eigenvalue
answer

False

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