Popular in Course
Popular in Physics 2
This 7 page Class Notes was uploaded by Dr. Carissa Rowe on Tuesday October 20, 2015. The Class Notes belongs to PHYS410 at San Diego State University taught by Staff in Fall. Since its upload, it has received 25 views. For similar materials see /class/225321/phys410-san-diego-state-university in Physics 2 at San Diego State University.
Reviews for PHYS410
Report this Material
What is Karma?
Karma is the currency of StudySoup.
You can buy or earn more Karma at anytime and redeem it for class notes, study guides, flashcards, and more!
Date Created: 10/20/15
Lecture 10 Outline The SHO 2 o Solvay talk Schrodinger and Born 0 stuck in an SHO ladder operators method 231 Ladder Operators warmup 0 Show that PAHCLW E thCAL w Zeroeth solution 0 Eventually we reach a point Where 1L1 CAL77D0 0 o a condition we use to nd 0 1 713 mums 0 0 2hmw d9 1dw0 mwaz and so 1dw0daz mw ada 0 d3 h 0 d2 h 0 Which has solution In 1amp0 7 L 512 some constant l we Ae x2 5 2 And Hm imam awe Em thus EO gm General solution a we can now generate the set of stationary states was Anlt gtw0ltxgt while En n w 0 Given the ground state solution and its energy mw 1amp0 exp 21 512 and E0 7M o the rst excited state is o remember also that H Lw E hwampib Hermitian conjugates 1 aj 2hmw IF 213 mm o ELi is the Hermitian conjugate of CALF 0 Since for any two functions f 13 95 we have fltxgtltaigltxgtgtdx amp f93 993d95 a disclaimer here f 13 95 must go to zero at 00 Algebraic Normalisation a Want coef cients Lwn annH and CAL77Dn dnwwl 0 First using the Schrbdinger equation H w nwn 1 1 hwampiamp i 5mm Mn Em A A 1 1 aia t 35 5W7 n i 0 Thus L Lwn mbn and L Lwn n 1mm NOW Ion Iwnll2das amnmmmx mamnfwndx n1wwndasn1 CAM n V n 1wn1 awn wa wn Ort honormality a We want to show that f wfnwnda 6mm a First we start with wnampawndx n wgwndx a but we can rewrite the above left hand side as Mmfmwndx mmmmndx m wmdx o thus mwfnwnda nwfnwnda 0 thus if m 75 n then must have f wfnwnda 0 0 thus if m n then must have f wfnwnda 1 0 So all of the SHO states are orthonormal
Are you sure you want to buy this material for
You're already Subscribed!
Looks like you've already subscribed to StudySoup, you won't need to purchase another subscription to get this material. To access this material simply click 'View Full Document'