A graph plots the real part and the imaginary part of the Gaussian bump against

PHYSICS · Multi-part · Fermi University Physics · Quantum Mechanics · Wave mechanics in one dimension · Wave mechanics in one dimension

Quantum Mechanics: From the Photon to the Hydrogen Atom, Ch The Schrödinger equation and the Born rule

Problem

A graph plots the real part and the imaginary part of the Gaussian bump

\Psi(x,0)=Ae^{-x^2/4a^2}e^{ik_0x}

against

x

, for the choice

k_0=\pi/(2a)

. Two points are marked and labelled with their coordinates:At

x=0

: the real part reads

A

and the imaginary part reads

0

.At

x=a

: the real part reads

0

and the imaginary part reads

0.779A

. ((a)) Using only these graph readings (not the formula for

\Psi

), compute

|\Psi|^2

x=0

and at

x=a

, as multiples of

A^2

. ((b)) The chapter's opening section states that

|\Psi|^2/A^2=e^{-x^2/2a^2}

falls to

e^{-1/2}=0.607

x=a

. Does your graph-reading answer for

x=a

agree?