In this worksheet, we will practice explaining the meaning of the terms in the Schrödinger equation and the general features of molecular wave functions.

**Q1: **

For a one-dimensional system, the potential energy function is described by . The SchrΓΆdinger equation for the system is:

- A
- B
- C
- D

**Q2: **

The kinetic energy operator for a one-dimensional system is:

- A
- B
- C
- D

**Q3: **

For the three-dimensional particle in a box system, the Hamiltonian is separable, i.e., . How can the total wavefunction of the system be expressed?

- A
- B
- C
- D

**Q4: **

The SchrΓΆdinger equation for the rigid rotor system must be solved with the spherical coordinate system. What is the correct expression for calculating the average value of , the component of the angular momentum?

- A
- B
- C
- D

**Q5: **

The solution of the SchrΓΆdinger equation for the rigid rotor system results in degenerate states for non-zero values of the angular momentum quantum number . For the energy level with , the degeneracy is:

**Q6: **

The SchrΓΆdinger equation for the rigid rotor system must be solved with the spherical coordinate system. For the of the orbital angular momentum , which of the following expressions gives the expectation value?

- A
- B
- C
- D

**Q7: **

In the solution of the SchrΓΆdinger equation for the rigid rotor system, what is the degeneracy of an energy level with angular momentum quantum number ?

**Q8: **

The solution of the SchrΓΆdinger equation for the hydrogen atom results in degenerate states for the principal energy levels characterized by the principal quantum number. For , what is the degeneracy?

**Q9: **

Wave functions for the hydrogen atom can contain nodes. The 5p orbital possesses:

- Afive angular nodes and three radial nodes.
- Btwo angular nodes and two radial nodes.
- Cone angular node and five radial nodes.
- Done angular node and three radial nodes.

**Q10: **

Wavefunctions for the hydrogen atom contain nodes. The 4d orbital possesses:

- Afour angular nodes and two radial nodes.
- Bthree angular nodes and one radial node.
- Cfour angular nodes and one radial node.
- Dtwo angular nodes and one radial node.

**Q11: **

The time independent form of the SchrΓΆdinger equation is given by:

- A
- B
- C
- D

**Q12: **

For a one-dimensional system, the potential energy function is described by . The SchrΓΆdinger equation for the system is:

- A
- B
- C
- D

**Q13: **

Which of the following is the correct form of the time-independent SchrΓΆdinger equation?

- A
- B
- C
- D