# Worksheet: The Schrödinger Wave Equation

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