Quantum II (PHYS 4410)Lecture 4

Spin ½ continued.

HWK 1 is due online at D2L by 5PM tomorrow.HWK 2 is due Wed. next week.

Physics Colloquium 4PM Today: Duane G1B20

Prof. Harry Nelson. Univ. of Calif. Santa Barbara“Light from Dark”

Consider three functions f(x) , g(y), and h(z) which obey the equation:f(x) + g(y) + h(z) = C = constant. How many of the functions must be constant?

A) f, g, and h must all be constants. B) One of f, g, and h, must be a

constant.C) Two of f, g, and h must be

constants.81

If H is a sum, Y is a product.

You have two spins, so you create a new hermitian operator:

( )total electron protonZ Z ZS S S

Therefore, you expect that the eigen vectors of this hermitian operator are:

A) A sum of the electron and proton eigen vectors.B) A product of the ele. and prot. Eigen vectors.C) Something else

You have two spin ½ objects and consider the sum of their z-components of spin:

( )total electron protonZ Z ZS S S

What is the maximum value you expect for the quantum number mtotal

A) ½B) 0C) 1D) 2E) Something else.

150

Suppose we represent a qubit so that:

What is the appropriate matrix operator for NOT?

A) B) C)

D) E) None of these

11

0

1 0

0 1

00

1

and

1 0

0 1

0 1

1 0

1 1

1 1

150

Given a qubit in a superposition state:

What is the effect of operating with NOT?

A) B) C)

D) E) None of these

a

b

1

0

b

a

a

b

0

1

What about (NOT) (NOT) ?