Quantum Mechanics and Atomic Physics 1
Quantum Mechanics and Atomic Physics 1 PHYS 3220
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This 2 page Class Notes was uploaded by Mrs. Peter Toy on Friday October 30, 2015. The Class Notes belongs to PHYS 3220 at University of Colorado at Boulder taught by Staff in Fall. Since its upload, it has received 7 views. For similar materials see /class/232119/phys-3220-university-of-colorado-at-boulder in Physics 2 at University of Colorado at Boulder.
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Date Created: 10/30/15
Formula Sheet for Exam 2 Steve and Oliver39s Crib sheet 2 2 The classical wave equation x V The timedependent Schrodinger Equation TDSE 911mm i 9211mm 9t 2m 2 if Vx1Px t The timeindependent Schrodinger Equation TISE IIux E ux or iazum 2m 8x2 Vxux Eux The standard deviation of an operator 0 arWa o wmJlt02gt ltogt2 The momentum operator Stationary states for a particle in an in nite square well running from X0 to Xa 2 I 2 2h2 u x 7s1n x E n n 2 a a 2mg 1 Statlonary states for a partlcle 1n a Harmonlc Osc lator potent1al Vx Emwz 14 ma 1 2 mm M x 7 7H 2395 n x E n12hw quotlzmlmng 5 h N Where Hn is the nth hermite polynomial with e g H1l Hz2 etc 4414 Draft new formulas for Exam 2 Fourier Transform formulae Plancherel s Theorem f x fdk Fk expikx Fk fdx fxexp ikx A useful form of the delta function 5x fexp k x dk Jxt52 hqI aq AVE 1m 39 m m 6x 1 6x 6x ERG 13W Wxt fdp 11gtptexpipxh ltIgtpt J17de lI xtexp ipxh 2am Momentum space wavefunction Positionmomentum commutator Di 13x ih d A A ltH Qgt assuming Q operator is independent of time Heisenberg Uncertainty Principle 0A 039 ltA 1 Postulate 4 Given a particle in state NP if you measure an observable Q the probability of measuring a particular value qn which must be one of the eigenvalues of operator Q with corresponding eigenfunction fngt is given by Probfind q Kt Ip2 Probfind q gt qdq Krq MK dq