- #1

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[tex](\Delta A)^2=<\psi|A^2|\psi>-<\psi|A|\psi>^2[/tex]

[tex]=<\psi|(A-<A>)^2|\psi>[/tex]

where A is an operator and [tex]\psi[/tex] is the wavefunction and [tex]<A>[/tex] is the expectation value of A

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- Thread starter lavster
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- #1

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[tex](\Delta A)^2=<\psi|A^2|\psi>-<\psi|A|\psi>^2[/tex]

[tex]=<\psi|(A-<A>)^2|\psi>[/tex]

where A is an operator and [tex]\psi[/tex] is the wavefunction and [tex]<A>[/tex] is the expectation value of A

- #2

Doc Al

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Just expand this expression, realizing that <A> is just a number. ([tex]<A> = <\psi|A|\psi>[/tex])[tex]=<\psi|(A-<A>)^2|\psi>[/tex]

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- #3

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thanks for quick reply! however im still not getting it. could you write it out expliitly please?

- #4

Doc Al

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[tex]<\psi|(A-<A>)^2|\psi> = <\psi|A^2 -2A<A> + <A>^2 |\psi>[/tex]thanks for quick reply! however im still not getting it. could you write it out expliitly please?

I'll let you do the rest.

- #5

Fredrik

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- #6

Doc Al

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I thought those bras and kets looked a bit off. :uhh: (Thanks, Fredrik!)

- #7

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I thought those bras and kets looked a bit off. :uhh: (Thanks, Fredrik!)

Must... not... say... I... prefer... bras... off... must... not say... to staff...ARGGGH.. Too late. Be gentle!

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