To memorize

Question 1

how do you expand|+z> in terms of |+x> and |-x>?

Answer 1

1/sqrt(2)|+x> + 1/sqrt(2)||-x>

Question 2

How do you expand|-z> in terms of |+x> and |-x>?

Answer 2

1/sqrt(2)|+x> - 1/sqrt(2)||-x>

Question 3

How do you expand|-x> in terms of |+z> and |-z>?

Answer 3

1/sqrt(2)|+z> - 1/sqrt(2)||-z>

Question 4

How do you expand|+x> in terms of |+z> and |-z>?

Answer 4

1/sqrt(2)|+z> + 1/sqrt(2)||-z>

Question 5

what is the x Pauli matrix in the z basis

Answer 5

0 1 1 0

Question 6

What is the y Pauli matrix in the z basis

Answer 6

0 -i i 0

Question 7

what is the z Pauli matrix in the z basis

Answer 7

1 0 -1 0

Question 8

Consider the 2x2 pauli matrices, how do you go from those to the spin operator matrices

Answer 8

multiply them by hbar/2

Question 9

What does the x Pauli matrix do to |+z>

Answer 9

|-z>

Question 10

What does the x Pauli matrix do to |-z>

Answer 10

|+z>

Question 11

What does the z Pauli matrix do to |-z>

Answer 11

• |-z>

Question 12

What does the z Pauli matrix do to|+z>

Answer 12

|+z>

Question 13

What is the position operator in terms of ladder operators for the harmonic oscillator

Answer 13

sqrt(hbar/(2mw) (a_dagger + a)

Question 14

What is the momentum operator in terms of the ladder operators for the harmonic oscillator

Answer 14

sqrt(hbarmw/2) (a_dagger - a)

Question 15

What is the commutator [X, P]?

Answer 15

ihbar

Question 16

What is the commutator [a_dagger, a]

Answer 16

1

Question 17

For the harmonic oscillator, what is the Hamiltonian written in terms of the ladder operators?

Answer 17

hbarw(a_dagger a + 1/2)

Question 18

What are the energy eigenvalue solutions for the infinite square well?

Answer 18

n^2pi^2hbar^2/(2mL^2)

Question 19

What are the energy eigenvalue solutions for the harmonic oscillator?

Answer 19

hw(n+ 1/2)

Question 20

What are the energy eigenvalue solutions for the harmonic oscillator?

Answer 20

-1/n^2(13.6eV)