Answered: Let the spin-1/2 particle be in an… | bartleby

Related questions

Question

2. Let the spin-1/2 particle be in an eigenstate of Sz, with eigenvalue 1/2. Compute the new state of the system when the system is rotated by an angle of 60◦. (a)about the z- axis (b)about the x- axis

Expert Solution

Trending now

This is a popular solution!

Step by step

Solved in 3 steps

SEE SOLUTION Check out a sample Q&A here

Blurred answer

Similar questions

3. For free particles in two dimensions, what is density of states (DOS) in low speed limit (=p²/2m), and in high speed limit (=pc)?
Is it possible for the z component of the orbital magnetic moment to be zero, but not the orbital angular momentum? Explain.
17. Please answer question throughly and detailed.
A hydrogen atom is located in an area where there is both a uniform magnetic field and a uniform electric field that are parallel to each other. a) write out the Hamiltonian of perturbation (ignore the spin of the electron). b) use perturbation theory in order to calculate the first order correction to the energy levels n=1,2 c) is there any degeneracy left? Compare with situations in which there is a magnetic field or only an electric field.
7. Consider a particle in an infinite square well centered at x = 0 in one of its stationary states. For this problem, you may look up any integrals. Some useful ones are given in Harris. a) Compute (x) and (pr) for arbitrary n. Do this by direct computation but then describe how you could have found these results using symmetry (the symmetry can either be symmetry in the physical system, such as the shape of the wave function, or symmetry related to the expectation value integral, such as the shape of the integrand). b) Using your answer to part a), show that the uncertainty in the momentum is Apx nh for arbitrary n. Do this two ways: (i) first by using your answer to part a) and directly computating (p2) (via an integral) and (ii) by using your answer to part a) and relating (p2) to the kinetic energy operator. c) Show that the uncertainty principle holds for the ground state. 2L -
4. Use the variational principle to estimate the ground state energy of a particle in the potential (∞0 x < 0 U(x) = \cx x≥0 Take xe-bx as a trial function.
4. Consider a quantum 3-it initially in the state |v) e Cº. Suppose that the 3-it undergoes a reversible evolution associated with the unitary matrix A, immediately after which a measurement of the observable B is performed. What is (B) for this measurement if 0 0 -i A = (0 1 1 0 0 0 -i 0 0 |v) and B = |? (Express your result as an explicit real number.)