# Tagged Questions

The quantum mechanical time evolution operator governs how observables and/or states evolve during finite time steps, and is always unitary. Use this tag for questions about the time evolution operator, or the different equations of motion in the Schrödinger/Heisenberg/Dirac pictures. For time-...

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### The formal solution of the Schrödinger equation

Consider the Schrödinger equation (or some equation in Schrödinger form) written down as $$\tag 1 i \partial_{0} \Psi ~=~ \hat{ H}~ \Psi .$$ Usually, one likes to write that it has a formal solution ...
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### Who is doing the normalization of wave function in the time evolution of wave function?

In the Schrodinger equation, at any given time $t$ we should jointly add another sub equation, like $$||\psi_t(x)|| = 1$$ where $\psi_t(x) = \Psi(x,t)$, and then try to solve the two equations ...
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### Time evolution in quantum mechanics

We know that an operator A in quantum mechanics has time evolution given by Heisenberg equation: $$\frac{i}{\hbar}[H,A]+\frac{\partial A}{\partial t}=\frac{d A}{d t}$$ Can we derive from this ...
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### Is it possible to derive Schrodinger equation in this way?

Let's have wave-function $\lvert \psi \rangle$. The full probability is equal to one: $$\langle \Psi\lvert\Psi \rangle = 1.\tag{1}$$ We need to introduce time evolution of $\Psi$; we know it in ...
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### How do I enforce the no-slip boundary condition in time dependent incompressible pipe flow?

This is a technical problem which must have been solved already. It won't be in beginners textbooks but there should be a solution somewhere. I welcome reading suggestions. Maybe someone with ...
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### Extending the ergodic theorem to non-equilibrium systems

I try to make this as short and concise as possible. For equilibrium systems in statistical mechanics, we have the Liouville's theorem which says that the volume in phase space is conserved when the ...