What do waves represent in QM?

[iScience]

i get that the Waves represent the probability density of the object, but a wave has a crest and a trough. What does the specifically does the trough represent? what specifically does the crest represent?

 

[DiracPool]

What does the specifically does the trough represent?

A low probability of finding a particle at that location.

what specifically does the crest represent?

A high(er) probability of finding a particle at that location.

 

[iScience]

that doesn't make sense.. if that's true... then what's the MAGNITUDE represent?..

there's magnitude, then there's polarity (ie, beyond the null point, that make up the trough and crest).

 

[king vitamin]

You referred to the "waves" as a probability density. The Born rule in QM is that the magnitude of the wave function is the probability density, so DiracPool probably assumed you meant the magnitude.

Are you referring to the sign of a wave function? One can multiply the total wave function by -1 and it will have no effect as long as one does so everywhere. The physically important aspect comes in if you have wave interference, where you can get a crest and a trough interfering to give zero magnitude. Once again, the crest and trough are interchangeable, it's their relative sign that matters.

 

[vanhees71]

In non-relativistic quantum mechanics wave functions represent the state of the system. It's the position representation of the state ket, i.e., assuming the Schrödinger picture of time evolution,
$$\psi(t,\vec{x})=\langle \vec{x}|\psi,t \rangle.$$
The physical meaning is given by Born's rule, according to which
$$P_{\psi}(t,\vec{x})=|\psi(t,\vec{x})|^2$$
is the probability density of the position of the particle at time $t$.