Recent content by Shredface

How do I show that the scalar product is time independent? I have: \frac{d}{dt}\int\Psi^{*}_{1}(x,t)\Psi_{2}(x,t)dx = 0 And have proceeded to take the derivatives inside the integral and using the time dependent Schrödinger eq. ending up with...

So the integral of zero is zero thus proving the initial statement. Yay! Cheers for the help guys, all seems so easy now!

How's this... E \Psi(x,t) = i\hbar \frac{\partial}{\partial t} \Psi(x,t), \Rightarrow E \Psi^*(x,t) = -i\hbar \frac{\partial}{\partial t} \Psi^*(x,t) Giving: \frac{\partial \Psi}{\partial t} = -\frac{iE}{\hbar} \Psi(x,t) and \frac{\partial \Psi^*}{\partial t} = \frac{iE}{\hbar}...

So I get: \frac{\partial}{\partial t} \left|\Psi\right|^2 = \Psi \frac{\partial \Psi^*}{\partial t} + \Psi^* \frac{\partial \Psi}{\partial t} What should I use for my wave function? \Psi\left(x,t\right) = Ae^{i(kx-wt)/\hbar} ?

Homework Statement Suppose you assume that you have normalised a wave function at t = 0. How do you know that it will stay normalised as time goes on? Show explicitly that the Schrödinger equation has the property that it preserves normalistion over time. Homework Equations From my notes I...

Homework Statement Find dz/dt where z = (x^2)(t^2) and x^2 + 3xt + 2t^2 = 1. 2. The attempt at a solution I really have no idea how to go about this, I've tried rearranging the second expression in terms of x but it's no help.