Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.

Please verify your account before proceeding.

In this lesson, we will learn how to explain 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 π£ ( π₯ ) = π π₯ . The SchrΓΆdinger equation for the system is:

Q2:

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

Q3:

For the three-dimensional particle in a box system, the Hamiltonian is separable, i.e., Μ π» = Μ π» ( π₯ ) + Μ π» ( π¦ ) + Μ π» ( π§ ) π₯ π¦ π§ . How can the total wavefunction of the system be expressed?

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 πΏ π₯ , the π₯ component of the angular momentum?

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 π . For the energy level with π = 1 , the degeneracy is:

Q6:

The SchrΓΆdinger equation for the rigid rotor system must be solved with the spherical coordinate system. For the π¦ - c o m p o n e n t of the orbital angular momentum πΏ π¦ , which of the following expressions gives the expectation value?

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 π = 2 ?

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 π = 3 , what is the degeneracy?

Q9:

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

Q10:

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

Q11:

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

Q12:

For a one-dimensional system, the potential energy function is described by π ( π₯ ) = 1 2 π π₯ 2 . The SchrΓΆdinger equation for the system is:

Q13:

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

Donβt have an account? Sign Up