Question

A particle of mass m is subject to a doubly infinite square well, with widths L, located at (a/2, a/2). The eigenstate wave functions for this are v(x, y) = L, = a and centre %3D %3D sin () sin ("). nyTy a) Find an expression for the position operator in bra-ket notation. b) Find an expression for the momentum operator in bra-ket notation. c) The particle is initially in the state |) : for position and momentum to find the expectation values of position and momentum for this (1, 2) + en/4 |2, 1)). Use the bra-ket operators state.

Answer 1

Solution : Given: A padlicle of mass m is subject to a doubly ing.ihile squre Well, with widths. la = ly za and Centere locuted at (al2, Al2). :: 9(114) j sin ( 1***) pensing mytoys @ Position de å ty ý 1. = Imraer hy> at = <) = {nx/xingy Ly} = {ny lvl ny) © <Px) = <nal Pe I hex <pu> - <nu l.pring> © 193 = (. s> te**, 12,13). Lx)= (4 belu) = [<0.012)\n) + <zollaleus] (118119)-(13)%25v2.mg ). sin (aur) de dy

- a Six sin ( a ). der = á Sve (1-сos (org lite lässing (y =12 - ä [-] similarly 211111211) = :. (o)= (3+) ==> simi lovely solving Joey, we get <i) = {P/1.14) - + [2121011a) <21/8el2v) + <121 px/211)eiteit1/ <11/82/12

<uz! relia) a Son ( 1 ) id som hade ) de ® in the same sin(ata) dan 21 Do a do dx da Similovely, <2.1/82/211) =0 <12/021211) - Cassino V-it) sin( 2017 ) elox - ** sin(). ( 27 ) cos( por de ih S[sin( 303 ) + sin (1923)te = alt som t son pou yo --it. [2]+(-2)] = -1.png (5) [24] - - xã = -8 its 34

</0/12) 3{**) \sin ( sury). Cornelio - cha [sin ( sub ) + 510 ( 12 )]dx -16x 89 3T a 2 .(Px) = ₃ [oto- sih celine te inta] 3a kPad = - 2025 <pu>= {4184/4). - } [rolpallie) K2,1 84/22) +202 /ecbu) e "4 keulada en L121P4/127= {211/24/2,17 -0

☺ 51,21841217 = {2011 Pelliz) = - Bich (Put = -2v2 it - 39 2