In this worksheet, we will practice representing the properties of quantum particles with probability wave functions using the Schrödinger wave equation.

Q1:

A wave function is evaluated at the rectangular coordinates in arbitrary units. What are the spherical coordinates of this position?

A

B

C

D

E

Q2:

A wave function of a particle with mass is given by
where .

Find the probability that the particle can be found
in the interval m.

Q3:

Given the complex-valued function , calculate .

Q4:

Which of the following is the expectation value of the position squared for a
particle that is in its ground state in a box of length ?

A

B

C

D

E

Q5:

Which of the following is the expectation value of the kinetic energy for a particle in the state when
confined to a region between 0 and ?

A

B

C

D

E

Q6:

A free proton has a wave function given by
,
where is measured in
meters and
in
seconds.

Find the momentum of the proton.

A kgโ m/s

B kgโ m/s

C kgโ m/s

D kgโ m/s

E kgโ m/s

Find the energy of the proton.

A J

B J

C J

D J

E J

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