Decide which of the following define a state of

PHYSICS · Multi-part · Fermi University Physics · Mathematical Methods for Physics · Quantum Mechanics · The formalism of quantum mechanics

The Structure of Quantum Mechanics, Ch Hilbert space and Dirac notation

Problem

\mathcal H

. For each that does, give the constant that normalises it. ((a)) The coefficient sequence

c_n=1/n

n=1,2,3,\dots

, against an orthonormal basis

\{|n\rangle\}

. ((b)) The coefficient sequence

c_n=n^{-1/4}

against the same basis. ((c)) The function

\psi(x)=(1+x^2)^{-1/4}

on the whole real line. ((d)) The function

\psi(x)=(1+x^2)^{-1/2}

on the whole real line.