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Why velocity in quantum mechanics is meaningless while we can always put v=p/m where p is momentum?

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- Thread starter hokhani
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- #1

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Why velocity in quantum mechanics is meaningless while we can always put v=p/m where p is momentum?

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Simon Bridge

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But you need to give us a context. Velocity does have meaning in QM, you just have to be careful about what you are talking about. Where did you hear/read that "velocity is meaningless"?

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- #4

Simon Bridge

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In QM a particle can be prepared in a state with a well defined velocity.

A wavepacket may have a group velocity.

The classical equations of motion hold for the associated QM expectation values.

In solid state, we can talk about the drift velocity of charges.

... and so on.

OTOH: the behavior of particles in a solid is usually handled statistically so properties for individual particles lose their meaning.

Also: It's usually more useful to use momentum directly: it has a handy relationship with position for instance. It also means we don't have to worry about whether the particle has mass or not.

So take your pick... could be any or none of these.

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Could you please tell me what makes semi-classical approach different from quantum approach?

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$$\left \langle v \right \rangle = \frac{d \left \langle x \right \rangle}{dt}=\frac{d}{dt}\int ^{\infty} _{- \infty} x \left|\Psi (x,t)\right| ^2 dx$$

I'll stress that this is not the velocity of the particle, but rather the expectation value.

- #7

Simon Bridge

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So the argument he was posing, in using classical ideas about velocity, mixed with quantum mechanical statistics, is neither classical nor quantum. And then he gave you a name.

Semi-classical is where quantum statistics get used to modify classical mechanics to make an approximation to the pure quantum case with more intuitive maths.

Usually there is a sense that half the system is quantized somehow ... i.e. a semi-classical treatment of the photoelectric effect would keep light as a continuous EM wave while quantizing the electron energies.

The pure quantum approach would be solving the schrodinger equation at some stage.

You didn't do that right?

For more detail, you can look it up.

http://en.wikipedia.org/wiki/Semiclassical_physics

http://link.springer.com/chapter/10.1007/978-3-540-70626-7_197#page-1

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