학술논문

Wavefunctions
Document Type
Chapter
Author
Source
Essential Quantum Mechanics, 2007, ill.
Subject
position representation
momentum representation
Gaussian
time evolution
free particle
wavepacket
bra-ket notation
Dirac notation
Quantum Physics
Condensed Matter Physics
Language
English
Abstract
This chapter focuses on a basic but systematic treatment of wavefunctions. By comparison with a spin 1/2 system, the concept of a wavefunction as a collection of coefficients is developed, followed by discussions of eigenstates, operators, and representations in the context of wavefunctions. Transformation from position to momentum representation is effected by a Fourier transform. This is developed next, and illustrated for a Gaussian. The discussion of phases and time evolution in earlier chapters is now applied to wavefunctions, and the time evolution of a free particle discussed. The concept of a wavepacket and its suitability for representing particles follows. A topic of some subtlety — and one which is discussed in detail — is the use of bra-ket (Dirac) notation for wavefunctions. The chapter closes with a short epilogue.

Online Access