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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