Does the Wave Function Predict the Most Likely Position of an Electron?

[Billyneutron]

Hi. I have a simple question-

Does the wave function describe probability of finding a particle in a certain state upon collapse of the wave function?

 

[arkajad]

Wave function upon a collapse can be as good as before collapse. Wave functions do not have to be destroyed by the collapse. Yet sometimes people destroy them by their unrealistic assumptions like, for instance, that the wave function collapses to a Dirac delta state.

 

[Billyneutron]

Thanks for the reply. My question is more general, though.

A particle in superposition collapses to one state. Does the wave function give any information/probability which "state" the particle will end up in following collapse?

 

[arkajad]

That depends on what is causing the collapse. The collapse does not happen by itself. It is caused by some measuring device. The state of your quantum system can be a superposition of two states and then collapse into a completely different third state - depending on the overall physical situation and also on some random factors.

 

[Fra]

A particle in superposition collapses to one state. Does the wave function give any information/probability which "state" the particle will end up in following collapse?

Yes, that's exactly that point of the wavefunction. As per the born rule, you get the conditional probability of obtaining a particular state after the collapse; given the information before the collapse.

The "collapse" itself, is in this sense nothing but an "information update", which by itself is an observer dependent event.

/Fredrik

 

[Billyneutron]

Thanks guys, and I appreciate your patience with me!

Consider this hypothetical overly-simplified example.
Let's say an electron can occupy two positions (double well) in a protein, separated by an energy barrier.

A wave function would then describe probability amplitudes of finding the electron in either position (or, rather, BOTH positions). Superposition of the electron in both positions is a necessity of the wave function..?

Since there is an energy barrier separating the double well, then there seemingly would be greater probability of finding the electron in the lower well than the higher energy well... and so, upon observation, the electron could be in either (lower energy, or higher energy via tunneling), however, since there is greater probability the electron will be observed in the lower energy well, then.. would you say- once an observation is made, the electron will be found in the lower energy well "more often than not"?

Again, thanks for your patience.. I'm a life science guy :)