Quantum Mechanics Demystified by David McMahon

Author:David McMahon
Language: eng
Format: epub, pdf
Tags: -
Publisher: McGraw-Hill Education
Published: 2013-04-23T00:00:00+00:00

The matrix representation in this basis is

We see that

and so

This is the completely mixed state for three dimensions. And so we have the bounds

where ρA is a pure state. The state ρm is a partially coherent state.

EXAMPLE 8-12

We work in a two-dimensional vector space with basis . Consider an ensemble of systems prepared in the following way. We have two quantum states

In the preparation of the ensemble, three-fourths of the states are prepared in state and one-fourth of the states are prepared in state .

(a) Write down the density operator for each individual pure state and .

(b) Write down the density operator for the ensemble.

(c) Express the density operator as a matrix with respect to the basis.

(d) Compute the trace.

(e) If a particle is drawn from the ensemble and a measurement is performed, what is the probability it is found in state ? What is the probability it is found in state ?

(f) Suppose there is another measurement with basis states . A particle is drawn from the ensemble, and a measurement is made in this basis. What is the probability of finding and what is the probability of finding ?

Download

Copyright Disclaimer:
This site does not store any files on its server. We only index and link to content provided by other sites. Please contact the content providers to delete copyright contents if any and email us, we'll remove relevant links or contents immediately.