Ok this probably only applies to anyone who has studied some quantum physics so if you haven't, you can read up or just totally ignore my post.

For those of you who have studied you were probably told that the wave function has no physical significance and that it is the square of the wave function which gives us information about probabilities etc.

However it is my belief that the wave function can give us very useful information and is not completely useless.

for example. consider the particle in the box. we have the formula

wavefunction = A sin (kx)

now if you were asked to locate a position of maximum probabilty. you would think it would involve squaring the wave function, differentiating this new function. followed by finding the value of x for which. d/dx = 0. then finding the second derivative to locate maxima.

however if you compare the two curves of sin x and sin^2 (x). it is clear that the maximum probability or the maximum of sin^2 (x), occurs whenever a stationary point is reached on the sin curve minimum or maximum. so to locate maximum probabilities,

it is simply a case of differentiating the wave function. then finding x values for which d/dx = 0. no need for a second differential either.

this doesn't give physical information (probabilities) but i think it is easy to dismiss the wave function as having no significance.

I have decided to make it a side project of mine to investigate the significance of the wave function and give it a fair trial.

watch this space.