# 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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### State collapse in the Heisenberg picture

I've been studying quantum mechanics and quantum field theory for a few years now and one question continues to bother me. The Schrödinger picture allows for an evolving state, which evolves through ...
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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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### 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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### How to describe time evolution in relativistic QFT?

I must confess that I'm still confused about the question of time evolution in relativistic quantum field theory (RQFT). From symmetry arguments, from the representation of the Poincare group through ...
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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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### 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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### The equivalence between Heisenberg and Schroedinger pictures

In quantum mechanics, the two pictures of Schroedinger and Heisenberg are taken as equivalent, where in the former wavefunctions are time variants and operators are not, and in the latter it is the ...
I was reading Feynman's Lectures III's Hamiltonian Matrix. There I found this property of Hamiltonian Matrix: The Hamiltonian has one property that can be deduced right away, namely, that $$H^*_{... 1answer 124 views ### Is continuous evolution from one eigenstate of operator O to another O-eigenstate possible? Eigenvectors associated with distinct values of an observable are orthogonal, according to quantum mechanics. Does this entail that a quantum system cannot continuously evolve from one eigenstate ... 2answers 693 views ### Time evolution of a reduced density matrix For a bipartite quantum system evolving under some master equation, is the time derivative of the reduced density matrix equal to the partial trace of the time derivative of the matrix? In other ... 2answers 139 views ### Time evolution in Quantum Mechanics abstract state space As I've learned the first postulate from Quantum Mechanics can be stated as follows: The states of a quantum system are described by vectors in a complex Hilbert space \mathcal{H}. The book ... 4answers 273 views ### Why do we consider the evolution (usually in time) of a wave function? Why do we consider evolution of a wave function and why is the evolution parameter taken as time, in QM. If we look at a simple wave function \psi(x,t) = e^{kx - \omega t}, x is a point in ... 2answers 2k views ### Why is time evolution unitary? Is the reason why the time evolution operator is unitary based on purely physical arguments, i.e. that the physical processes that an isolated system undergoes shouldn't depend on any particular ... 1answer 80 views ### Why does tr \ e^{-\frac{i}{h}\hat{H}t}= \int d^nr \left< \textbf{r}| e^{-\frac{i}{h}\hat{H}t} | \textbf{r} \right> hold? I would like to consider the trace of the time evolution operator e^{-\frac{i}{\hbar}\hat{H}t} Apparently in single-particle quantum mechanics is can be represented as$$ tr \ e^{-\frac{i}{\hbar}\...
From $$m\boldsymbol{\ddot{r}}=\boldsymbol{\hat{r}} f(r)$$ I can get $$r''-r \theta '^2=-\frac{k}{m r^2}$$ $$2 r' \theta '+r \theta ''=0$$ Now it seems that all the books tells me the method to solve ...