3
$\begingroup$

I want to look at the complex wave function $\psi$ in quantum mechanics.

If a complex number $a + bi$ is multiplied by $i$ it is rotated by 90 degree in the complex plane.

What does this mean for a complex scalar field, i.e. the wave function $\psi$?

I know, that $i\psi$ is as well a solution of the Schrödinger equation, because it is a linear differential equation.

My questions are:

  • What are the physical consequences, if one multiplies the wave function by $i$?
  • Are there any examples of actual experiments/phenomena, where something like that happens?
  • How can I depict the multiplication of the wave function by $i$?
$\endgroup$
5
$\begingroup$

There's no physical consequence in multiplying a wave function $\psi$ by a phase factor $e^{i\phi}$. Since in quantum mechanics we're interested in probabilities where the wave function appears always as $|\psi|^2$, the two wave functions $$\psi\qquad e^{i\phi}\psi$$ yield exactly the same physical results.

Multiplying by $i$ falls in this category since $e^{i\pi/2}=i$.

| cite | improve this answer | |
$\endgroup$
  • 4
    $\begingroup$ That's true. I only want to add that phase is only important when dealing with many wavefunctions. If two wavefunctions interact, their relative phase is important. But for a lonely $\psi$ it is meaningless $\endgroup$ – FGSUZ Jul 11 at 21:58
  • $\begingroup$ @FGSUZ Yeah, that's a very good point. $\endgroup$ – Local Mathmatician Jul 11 at 22:07

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.