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Quantum Mechanics$
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P.J.E. Peebles

Print publication date: 2019

Print ISBN-13: 9780691209821

Published to Princeton Scholarship Online: May 2021

DOI: 10.23943/princeton/9780691209821.001.0001

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Abstract Linear Space of State Vectors

Abstract Linear Space of State Vectors

Chapter:
(p.175) Chapter 3 Abstract Linear Space of State Vectors
Source:
Quantum Mechanics
Author(s):

P.J.E. Peebles

Publisher:
Princeton University Press
DOI:10.23943/princeton/9780691209821.003.0003

This chapter discusses abstract linear space of state vectors. The wave mechanics presented in the previous chapter is easily generalized for use in all the applications of quantum mechanics explained in this book. In particular, to take account of spin, one just replaces the wave function with a set of functions, one for each possible choice of the quantum numbers of the z components of the spins of the particles. However, as the chapter shows, it is easy to adapt the wave mechanics formalism to the more general scheme that represents the states of a system as elements of an abstract linear space rather than a space of wave functions. This approach has the virtue that one can explicitly see the logic of the generalization of the wave function to take account of spin, and this is the road to other generalizations, like quantum field theory.

Keywords:   abstract linear space, state vectors, wave mechanics, quantum mechanics, spin, wave functions, wave mechanics formalism

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