Where does negative probability go?

[questionposter]

If you graph the actual oscillation of a sub-atomic particle, it oscillates between positive crests of probability and negative ones, but where is it oscillating into when at the present time it is oscillating at negative probability? Is it oscillating in some other dimension? Or do you use the absolute value?

[IM Egdall]

Are you thinking of the amplitude? They can be positive or negative. You add the amplitudes then square the result. This is the probability of finding the particle in a certain location. And since you square, it is always positive.

[swansont]

The wave function can even be imaginary, but has no physical significance. As IM Egdall points out, the probability is the square (where this means the wave function multiplied by its complex conjugate)

[questionposter]

The wave function can even be imaginary, but has no physical significance. As IM Egdall points out, the probability is the square (where this means the wave function multiplied by its complex conjugate)

 

So if it doesn't have physical significance, then does that mean when it's oscillating as to exist where it would be in negative probability, it doesn't physically exist?

[Fuzzwood]

It doesn't have a negative probability.

[questionposter]

It doesn't have a negative probability.

 

a sine wave does not have different signs at different places?

Edited March 24, 2012 by questionposter

[ajb]

The wave function [math]\Psi[/math] itself is not the probability density. The probability density is given by [math]|\Psi|^{2}[/math] as already stated.

[Xittenn]

If you graph the actual oscillation of a sub-atomic particle, it oscillates between positive crests of probability and negative ones, but where is it oscillating into when at the present time it is oscillating at negative probability? Is it oscillating in some other dimension? Or do you use the absolute value?

 

Are you referring to the magnetic quantum number?

Edited March 24, 2012 by Xittenn

[ajb]

a sine wave does not have different signs at different places?

 

Think about the function [math]|\sin(x)|^{2}[/math].

[questionposter]

The wave function [math]\Psi[/math] itself is not the probability density. The probability density is given by [math]|\Psi|^{2}[/math] as already stated.

 

Well I don't see where it's already stated, but if its absolute value that solves it.

[mississippichem]

Well I don't see where it's already stated, but if its absolute value that solves it.

 

It's all about the choice of norm.

taxicab vs. 2-norm in QM

 

I enjoyed this article very much myself.

Edited March 24, 2012 by mississippichem

[timo]

Well I don't see where it's already stated [that the square of the magnitude is being taken], but if its absolute value that solves it.

 

It's been "already stated" around here:

Are you thinking of the amplitude? They can be positive or negative. You add the amplitudes then square the result. This is the probability of finding the particle in a certain location. And since you square, it is always positive.

and here:

The wave function can even be imaginary, but has no physical significance. As IM Egdall points out, the probability is the square (where this means the wave function multiplied by its complex conjugate)

 

iow: It has been explicitly mentioned in 100% of the replies you got until you re-posted here - and in almost half of all of the sentences therein. I think you should read replies you get a bit more carefully - to say the least.

[questionposter]

It's been "already stated" around here:

 

and here:

 

 

iow: It has been explicitly mentioned in 100% of the replies you got until you re-posted here - and in almost half of all of the sentences therein. I think you should read replies you get a bit more carefully - to say the least.

 

It seemes as though all of those posts were based off of a guess that I was talking about the "amplitude" of a wave rather than the actual oscillation of a particle. If in the equation to describe how a particle oscillates over time includes that a critical component is "squared" as to always have a positive result, then it should be fine.

Edited March 24, 2012 by questionposter

[Cap'n Refsmmat]

It seemes as though all of those posts were based off of a guess that I was talking about the "amplitude" of a wave rather than the actual oscillation of a particle. If in the equation to describe how a particle oscillates over time includes that a critical component is "squared" as to always have a positive result, then it should be fine.

Your original post talked about "positive crests of probability and negative ones", but the probability density function is [imath]|\Psi|^2[/imath], and cannot have negative crests, as pointed out before.

 

I don't know what you mean about amplitude vs. "actual oscillation." Your terms don't really make sense.

[questionposter]

Your original post talked about "positive crests of probability and negative ones", but the probability density function is [imath]|\Psi|^2[/imath], and cannot have negative crests, as pointed out before.

 

I don't know what you mean about amplitude vs. "actual oscillation." Your terms don't really make sense.

 

Well I thought he had meant literally just some pattern of the amplitude of a given wave, but I was talking about like the whole actual particle wave oscillating through time.