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- Thread starter Muthumanimaran
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It follows that [itex]\psi^*(x)\psi(x)[/itex] is the so called probability density. It is nothing but the function that, when integrated, gives you the probability itself.

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As for what ψ* means, it's the complex conjugate of the wavefunction... but of course you already know that. If you're looking for a nice intuitive way to interpret the physical meaning of the phase of a wavefunction, then I'm afraid I don't think that there is one.

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Exactly, this is just how the mathematical formalism of Quantum Mechanics works.As for what ψ* means, it's the complex conjugate of the wavefunction... but of course you already know that. If you're looking for a nice intuitive way to interpret the physical meaning of the phase of a wavefunction, then I'm afraid I don't think that there is one.

- #5

ChrisVer

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One quantity that is for sure real is [itex] \psi^{*} \psi [/itex] and nothing is "lost" from [itex]\psi[/itex]'s initial parameters (if for example you write [itex]\psi=a+ib[/itex] the result will contain both a and b...

Another example in which you can see that, is when you have [itex]\psi[/itex] real, where you don't need the complex conjugate and just take the square....

In fact the complex conjugate's "meaning" (mathematical) becomes clearer when you start working on the states in vector spaces... The conjugate appears as a relation between the bras and kets, and thus between the vector and its dual space.

- #6

bhobba

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Its got to do with the bra-ket notation:Let ψ be a wavefunction describes the quantum state of a particle at any (x,t), What does ψ* i.e, the complex conjugate of a wavefunction means?

http://en.wikipedia.org/wiki/Bra–ket_notation

The wavefunction is looked at as the Ket - its conjugate as the Bra - apply a Bra to a Ket and square it to get probabilities - that's the Born rule.

At a deeper level states are not actually Bra's or Kets - they are really operators - what are normally referred to as states have a special name called pure.

At an even deeper level again it is seen states are really what's required so we can work out probabilities of the outcomes of observables - this is the important Gleason's Theorem (the key assumption is what is known as non contextuality you may have heard about):

http://en.wikipedia.org/wiki/Gleason's_theorem

It's a devil of a thing to prove however so its not usually talked about much at the beginning level despite its importance.

There is a variant that is much easier to prove and some people use it as the foundation of QM eg:

http://arxiv.org/pdf/quant-ph/0205039v1.pdf

Anyway that will take you to a pretty advanced level. For now what I would do is get a hold of Ballentine:

https://www.amazon.com/dp/9810241054/?tag=pfamazon01-20&tag=pfamazon01-20

Its mathematically quite a bit more advanced than Griffiths. But hold onto your nerves and give the first 3 chapters a read. You wont likely understand too much of the detail, but, hopefully, fingers crossed, you will get the gist so that things are a lot clearer, and Griffiths will be easier. Once you have finished Griffiths you can move onto Ballentine.

Thanks

Bill

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- #7

UltrafastPED

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ψ is an element of a Hilbert space; ψ* is an element of it's dual space.

The Dirac bra-ket notation makes use of this: |ψ> is an element of the Hilbert space, and <ψ| is it's dual.

Following the general conventions for vector spaces with an inner product, we have <ψ|ψ> is the inner product, and it generates a real number.

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