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Dahaka14
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Homework Statement
Two identical bosons are found to be in states [tex]|\phi>[/tex] and [tex]|\psi>[/tex]. Write down the normalized state vector describing the system when [tex]<\phi|\psi>\neq0[/tex].
Homework Equations
The normalized state vector for two bosons with [tex]<\phi|\psi>=0[/tex], using the fact that [tex]|\psi>\otimes|\phi>=|\psi\phi>[/tex], is:
[tex]\frac{1}{\sqrt{2}}(|\psi\phi>+|\phi\psi>)[/tex].
The Attempt at a Solution
So I thought the new normalization would be to do:
[tex]1=A^{2}(<\psi\phi|+<\phi\psi|)(|\psi\phi>+|\phi\psi>)
=A^{2}(<\psi\phi|\psi\phi>+<\phi\psi|\phi\psi>
+<\psi\phi|\phi\psi>+<\phi\psi|\psi\phi>)
=A^{2}(2+C+C^{*})[/tex]
where C is a complex number. Since in general [tex]C=a+bi[/tex] where a is real and b is imaginary, [tex]C+C^{*}=(a+bi)+(a-bi)=2a[/tex]. Thus, the new, normalized state would be
[tex]\frac{1}{\sqrt{2(1+a)}}(|\psi\phi>+|\phi\psi>)[/tex]. I am not very confident with my answer, could someone please help me?
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