What causes "Wave Function Collapse" ?

[Widdekind]

What causes WF collapse ? In the Schrodinger Wave Equation, wouldn't an imaginary potential cause, at least on its own, WFs to exponentially grow (positive imaginary, same sign as time derivative) or exponentially shrink (negative imaginary, opposite sign from same). Could that, conceivably, have something to do with the "collapse of WFs" during observation & measurement ?

 

For example, using the 3D Dirac Delta Function ∆(x), the imaginary PE field Î(2∆(x)-1) could conceivably cause a wave function to exponentially grow at x, whilst exponentially shrinking away everywhere else (?).

[Widdekind]

Merely as a mathematical question, imagine replacing the Dirac Delta Function, in the above formula, with the Wave Function of some stable (bound) state (in one of the atoms in the detector), into which you "wanted" an incoming electron to collapse. For example, something along the lines of the standard hydrogen atom WFs. Mathematically speaking, wouldn't that "make", "force", or "hammer" the electron's own WF into the desired bound state ?

 

For example, wouldn't the imaginary potential ¡ ( 2 ¥_1s - 1 ) "grow" the electron WF into ¥_1s (~ e^r / r) ?? (If you multiplied that unit-less formula, by the Planck Energy, wouldn't it "grow" the electron WF, into the desired bound state, in a time of order the Planck Time ??) Of course, the standard Overlap Integral < ¥_e | ¥_1s > would also seem to yield a probability, of the electron (in ¥_e) appearing in the desired bound state (in ¥_1s). But, how could you turn that probability into a percentage chance of "collapse" into said bound state ??

[Bob_for_short]

It is not possible to obtain a "deterministic evolution" of the wave function like "collapse" into one specific state. A wave function describes the probability amplitude of different outcomes, and this is very good! This is what we need. What to do with a theory capable of describing only one of possible outcomes?

Edited March 12, 2010 by Bob_for_short

[swansont]

But, how could you turn that probability into a percentage chance of "collapse" into said bound state ??

 

That's what the probability is.

[Amr Morsi]

When you use a potential function in time (such as step up or step down) the schrodinger equation may give you a collapsed wave function or a generated one. But, in general, Schrodinger Equation gives stationary states when the potential energy (V) is not function in time, and the solution is obtained by SOV Method.