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Question 1: 20 points 1. An electron is at rest at the origin, in the presence of a magnetic field whose magnitude (B0) is constant but whose direction rides around at constant angular velocity ω on the lip of a cone of opening angle α: B(t) = B0[sin(α) cos(ωt)ˆi + sin(α) sin(ωt)ˆj + cos (α)ˆk]                                                         (1) 1a) Write the formula for the Hamiltonian for a particle with spin coupled to a magnetic field. (You only need to write the coupling Hamiltonian.)[5 points] 1b) Construct the 2 × 2 Hamiltonian matrix for this system. [5 points] 1c) Use first-order time-dependent perturbation theory to calculate the approximate probability of a transition from spin up (the initial state) to spin down, as a function of time. [5 points] 1d) State the criterion on the strength of the field that determines whetherperturbation theory is applicable in this case. [5 points]  

Question 5: 15 points 5. The scattering of a quantum particle off a potential V (x) can be treated by using the integral form of the Schrodinger equation in one dimension: ψ(x) = ψ0(x) − (im/

Question 4 – 15 points 4. Some radioactive nuclei, e.g. Phosphorus-32, emit electrons (“beta radioactivity”). Here we consider if Gamow’s model of radioactivity can be applied to understand beta emission. 4a) As in the case of alpha emission, consider the electron to be trapped inside the original nucleus in a square well. Outside the square well, the electron will feel the Coulomb force due to the final nucleus. Write an expression for the energy of the electron as a function of the distance from the nucleus. [5 points] 4b) Sketch the potential of part a). [5 points]   4c) Discuss if Gamow’s model can be applied to beta decay. [5 points]

While there are no specific examples of science as a way of knowing in the Bible, research is important to God.

In a study of the effect of caffeine on test performance, test performance would be considered the independent variable.

You are meeting with a client for the first time. (1) After greeting the client and sitting down in your office, you explain the risks, benefits, and alternatives of counseling. (2) You also discuss confidentiality and the situations in which you would have to break confidentiality as a mandated reporter. (3) After the client agrees to continue the conversation, you start asking the client questions about why they are seeking counseling, as well as questions about other psychosocial aspects. (4) Approximately 30 minutes later, you start to form a hypothesis about how the client’s presenting problems came to be. (5) In addition, based on the information the client presented, you believe the client has Major Depressive Disorder. (6) You share all of this information with your client. (7) You discuss your expertise in working with depression and other mood disorders, and you and the client agree to continue working together. (8) You also explain your expertise in cognitive-behavioral therapy and what the approach entails, including specific techniques that you may use in therapy. (9) Your client agrees to try the CBT approach in counseling. (10) You schedule the next session and say good-bye. What is the difference between segments 4 and 5?

There are five phases in the counseling process. In the phase of ______________, the therapist and client say goodbye to each other and work through issues that may come up.

Psychologists provide services with populations and in areas only within the boundaries of their _______________, based on their education, training, supervised experience, consultation, study, or professional experience.

Which of the following pieces of information should be provided to all clients as part of the informed consent process?

What is the reference angle for