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The Eggman
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Concerning expectation values...
Also, the derivation in terms of bra-ket rather than wage function would be appreciated.
Where [tex]\psi[/tex] is the system state
Knowing that <A>[tex]\psi[/tex]=<[tex]\psi[/tex]|A|[tex]\psi[/tex]>
And A is comprised of a complete eigenvector set [tex]\phi[/tex]j w/ corresponding eigenvalues aj
How do you derive <A>[tex]\psi[/tex]=[tex]\sum[/tex]aj|<[tex]\psi[/tex]|[tex]\phi[/tex]j>|^2 ?
Additionally, (unrelated to above)
if |[tex]\psi[/tex]> is comprised of component states |[tex]\phi[/tex]>,
And <[tex]\phi[/tex]|[tex]\psi[/tex]>=the relevant expansion coefficient (probability)
What is the value of <[tex]\psi[/tex]|[tex]\phi[/tex]>? The complex conjugate of the expansion coefficient?
Thanks!
http://en.wikipedia.org/wiki/Expectation_value_(quantum_mechanics )
Also, the derivation in terms of bra-ket rather than wage function would be appreciated.
Where [tex]\psi[/tex] is the system state
Knowing that <A>[tex]\psi[/tex]=<[tex]\psi[/tex]|A|[tex]\psi[/tex]>
And A is comprised of a complete eigenvector set [tex]\phi[/tex]j w/ corresponding eigenvalues aj
How do you derive <A>[tex]\psi[/tex]=[tex]\sum[/tex]aj|<[tex]\psi[/tex]|[tex]\phi[/tex]j>|^2 ?
Additionally, (unrelated to above)
if |[tex]\psi[/tex]> is comprised of component states |[tex]\phi[/tex]>,
And <[tex]\phi[/tex]|[tex]\psi[/tex]>=the relevant expansion coefficient (probability)
What is the value of <[tex]\psi[/tex]|[tex]\phi[/tex]>? The complex conjugate of the expansion coefficient?
Thanks!
http://en.wikipedia.org/wiki/Expectation_value_(quantum_mechanics )
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