Transcript Winter 2008 Physics 315 / 225

Winter 2008
Physics 315 / 225
Proposed title: Quantum Mechanics I
This course will be a prerequisite for
Phys. 248B Relativity/Particles/Symmetry (Spring)
Phys. 324 Quantum Mechanics (Autumn)
http://depts.washington.edu/jrphys/p315W08.html
Instructor: J. Rothberg, Office B207 Phone 543-2989
Office Hour: Tuesday at 1:30 [email protected]
Other office hours and discussion sessions to be announced.
Jan. 7, 2008
Outline 1
Polarization of Light
Classical description (E field)
Linear polarization
Intensity transmitted through Polaroid sheets
Circular Polarization
Description in terms of States
Photons
Agreement with classical picture
State vectors
Amplitude and Probability
Jan. 9, 2008
Photons (E=hf recall photoelectric effect)
State vector description of polarization
State of photon after a Polaroid sheet
Agreement with classical picture ( intensity proportional to cos2 q )
Probability
State Vectors
>
<x|
|x
Dual vectors
Inner product
Amplitude and Probability
Example: Circularly Polarized Light through a Polaroid sheet
TA office hours in Room B042:
Dan Bolton:
Mat Steuck
Tuesday 9:30 and 3:30
Monday 1:30 and Tuesday 2:30
First HW posted on webpage: due next Wednesday
Polarization of Light
Classical picture
Intensity is proportional to E
2
Component of E along transmission axis is transmitted
After a Polaroid sheet the direction of E is along the transmission axis
Photon picture
The intensity is proportional to the number of photons (E=hf for each photon)
A photon is transmitted with some Probability
(depends on initial photon state and on transmission axis)
After a Polaroid sheet we know the polarization state of the photon
Question:
can we determine the state of a single photon?
Jan. 11, 2008
Example: Circularly Polarized Light through a Polaroid sheet
Quantum Cryptography
Cryptographic Key (classical)
Reminder: photons and Polaroid sheets
Quantum Key Distribution – the BB84 protocol
Alice sends photons to Bob
Why an eavesdropper, Eve, is detectable
TA office hours in Room B042:
Dan Bolton:
Mat Steuck
Tuesday 9:30 and 3:30
Monday 1:30 and Tuesday 2:30
my office hours: Tuesday 12:30 to 2:30 or by appt. Room B207
First HW posted on webpage: due next Wednesday
Jan. 14, 2008
Particle and Wave nature of electrons
Electron Intrinsic Angular Momentum (Spin); Spin 1/2
Magnetic Moment, Bohr magneton, mB
Force on Magnetic Moment in inhomogeneous Magnetic Field
Stern-Gerlach experiments
(analogy to Polaroid or Calcite)
Basis States for spin
Superposition of states
TA office hours in Room B042:
Dan Bolton:
Mat Steuck
Tuesday 9:30 and 3:30
Monday 1:30 and Tuesday 2:30
my office hours: Tuesday 12:30 to 2:30 or by appt. Room B207
First HW posted on webpage: due next Wednesday
Strongly suggested reading for this week
From coursepak
McIntyre. Sections 1.1, 1.2, 1.3
French and Taylor Chapter 7
Le Bellac section 3.2.1 3.2.2 3.2.3
From “Notes I” on class web page
through section 2.2
4.1.1
Jan. 16, 2008
Basis States for spin
>
>
|+ and |-
Superposition of states; measure x component and y component of m
Similarities and differences: spin 1/2, polarization of photons
Expansion in basis states
Projection Operators
Matrix Representation of states and operators
Additional TA office hour in Room B125:
Wei Chen
Friday at 1:30
Jan. 18, 2008
Comment on homework
Matrix Representation of states
Postulates of QM
Projection Operators
|+
><+|
Operators
Average Value
S an Pn
Additional TA office hour in Room B125:
Wei Chen
Friday at 1:30
Jan. 23, 2008
Operators; matrix representation
Probability is square of inner product of
“beam state” and “measurement state”
|<SG|beam>|2
Average Value
S an Pn
Expectation value:
<y|A|y>
Spin Operators: Sx, Sy, Sz
Eigenvalue, Eigenstates:
A|y>=l|y>
Jan. 25, 2008
Superposition vs. Mixture
Average Value
S an Pn
Expectation value:
<y|A|y>
Spin Operators: Sx, Sy, Sz
Eigenvalue, Eigenstates:
A|y>=l|y>
Exam: Friday Feb. 1 on
HW I, II, III, practice problems
You will be given a formula sheet (see example on web page)
Monday, Tuesday
office hours as usual (see web page)
Thursday in B125
Wei 1:30
Mat 2:30
Dan 3:30
me
11:30 in B207 or B206
no office hour Friday.
Jan. 28, 2008
Eigenvalue, Eigenstates:
A|y>=l|y>
Spin Operators: Sx, Sy, Sz
States and directions in space. Bloch Sphere
Hermitian Operators
properties
Exam: Friday Feb. 1 on
HW I, II, III, practice problems
You will be given a formula sheet (see example on web page)
extra office hours this week
Jan. 30, 2008
HW Review
S2
Review
Commutation Relations
Exam: Friday Feb. 1 on
HW I, II, III, practice problems
You will be given a formula sheet (see example on web page)
extra office hours this Thursday
Feb. 4, 2008
Exam comments.
Review session schedule
S2
Commutation Relations, Simultaneous Eigenstates
Torque on Magnetic Moment
Energy of Magnetic Moment in Magnetic Field
Schrodinger Equation