3. Let Ê and Ê be the position and linear momentum operators of a single particle, respectively. The corresponding repre

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3 Let E And E Be The Position And Linear Momentum Operators Of A Single Particle Respectively The Corresponding Repre 1 (54.68 KiB) Viewed 41 times

3. Let Ê and Ê be the position and linear momentum operators of a single particle, respectively. The corresponding representations in one-dimensional position space are Ñų = rų(x) y = -ihdy(x) dir where x is position and is a wavefunction. a) Find the commutator [*, f] Consider the case of a particle of mass m in a 1-D box of length L, where the wavefunctions are VŽ sin(knx), 0<x< 1 0, otherwise - { V7-, = kn пл. nez, n > 0 L What is the b) Show that Un is an eigenfunction of the kinetic energy operator P2 corresponding eigenvalue? 2m c) Find < Ê>. d) Find < > e) Find < 2 >