Question: Suppose that the wave function for a system can be written as and that Ï 1 (x), Ï 2 (x), and Ï 3 (x) are

Suppose that the wave function for a system can be written as

w(x) = 2+ 3i 9(x) + Ø3(x) 222(x) +

and that φ1(x), φ2(x), and φ3(x) are orthonormal eigenfunctions of the operator ˆE kinetic with eigenvalues E1, 2E1, and 4E1 respectively.

a. Verify that ψ (x) is normalized.

b. What are the possible values that you could obtain in measuring the kinetic energy on identically prepared systems?

c. What is the probability of measuring each of these eigenvalues?

d. What is the average value of E kinetic that you would obtain from a large number of measurements?

w(x) = 2+ 3i 9(x) + 3(x) 222(x) +

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