HYDROGEN ATOM
A photon emitted by a hydrogen atom as a result of a transition from state n to state m is observed. It is found to have an energy of 1.9 eV. The transition n--> m is

2 --> 1
3 --> 2
3 --> 2
3 --> 1
3 --> 1
2 --> 1

STATEMENT
A famous physicist once stated that "...nobody understands quantum mechanics." Who was he?

Paul Dirac
Wolfgang Pauli
Wolfgang Pauli
Richard Feynman
Richard Feynman
Paul Dirac

MATTER WAVE
A particle with a mass of 1 mg moves with a velocity of 1 mm per second. As a matter wave, its wavelength is

6.6x10^-16 nm
6.6x10^-16 nm
6.6x10^-8 nm
6.6x10^-8 nm
6.6 nm
6.6 nm

DISPERSION RELATION
The dispersion relation for a quantum particle moving in free space is

independent of the momentum p.
proportional to p.
proportional to p.
independent of the momentum p.
proportional to p2.
proportional to p2.

EIGENFUNCTIONS
The eigenfunctions belonging to different eigenvalues of the Hamiltonian are always

normalized
orthogonal to each other.
orthogonal to each other.
normalized
real.
real.

QUADRATIC MATRIX
Consider a quadratic matrix A where all matrix elements are real valued. Which statement is correct?

The eigenvalues are non degenerate.
The eigenvalues are non degenerate.
If a is a complex eigenvalue of A, then also the complex conjugate a*.
If a is a complex eigenvalue of A, then also the complex conjugate a*.
All eigenvalues of A are real.

DOUBLE WELL POTENTIAL
Due to tunneling, the ground states of a double well potential are splitted by an energy of 4 μeV. The period of resulting oscillation of a wave packet

1 nanosecond
1 femtosecond
1 picosecond
1 picosecond
1 femtosecond
1 nanosecond

MORSE POTENTIAL
The energy eigenvalues of the harmonic oscillator are equidistant. For a Morse oscillator the eigenvalues

are also equidistant.
are also equidistant.
increase with increasing energy.
increase with increasing energy.
decrease with increasing energy.
decrease with increasing energy.

NODES
In a book you find a figure showing the six lowest eigenfunctions of a one dimensional potential. How many nodes do you see on this figure?

10
21
15
10
21
15

ONE-DIMENSIONAL BOX POTENTIAL
A particle is confined to a box. If the size of the box is increased, the energy

increases.
decreases.
decreases.
increases.
is not changed.
is not changed.

CHAPTER 5

ANGULAR MOMENTUM
The operators Lzand L2 commute. What can be said about the product of their uncertainties?
It is equal to zero.
It must be larger than hbar/2.
It can be made equal to zero.
It is equal to zero.
It must be larger than hbar/2.
It can be made equal to zero.

QUADRATIC BOX POTENTIAL
Which eigenvalues of a two dimensional quadratic box potential are characterized by the two quantum numbers n and m? Which of the following pairs of states are degenerate?

(n,m)=(5,4) and (n,m)=(7,1)
(n,m)=(5,4) and (n,m)=(7,1)
(n,m)=(3,8) and (n,m)=(4,7)
(n,m)=(7,4) and (n,m)=(1,8)
(n,m)=(7,4) and (n,m)=(1,8)
(n,m)=(3,8) and (n,m)=(4,7)

RADIAL WAVE FUNCTIONS
For a given eigenvalue of the hydrogen atom you can find altogether 49 different eigenstates. What is the largest number of nodes found in their radial wave functions?

64
64
6
6
48
48
All eigenvalues of A are real.

HYDROGEN ATOM A photon emitted by a hydrogen atom as a result of a...