Hi pf, I am having trouble with understanding some of the steps involved in a mathematical proof that a normalized wavefunction stays normalized as time evolves. I am new to QM and this derivation is in fact from "An introduction to QM" by Griffiths. Here is the proof: I am fine with most of the maths but I am struggling with a few points: Equation 21. He refers to this later and says "Ordinarily we need to justify taking a derivative inside an integral, but we can console ourselves with the knowledge that for any wave function for which this is not a valid operation, that function is also not a possible description of a physical state (for one reason or another)". Why do you need to justify taking a partial derivative inside an integral? Is this not normally a valid operation? Equation 25. I really don't understand how you can set a second derivative of a function equal to a first derivative? He says further on that the expression in the brackets at the start of equation 25 can be expressed as a single derivative - that doesn't make any sense to me why you can do this? Equation 26. Why is there no integral sign on the right hand side of the equation? The expression on the right hand side is the partial derivative of psi squared with respect to time (as shown in equation 22) whereas they are implying the right hand side of equation 26 is the integral of the partial derivative with respect to time of psi squared (i.e. the integration has been done hence no integral sign)? Thanks for any help!