# Questions tagged [time-evolution]

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-independent Hamiltonians, the time evolution operator is simply exp(-iHt).

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### A question in Dirac article about Dirac equation about a sentence

Why it is said $W$ should be linear partial time derivative so that wave function could be determined by initial wave function?
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### Quantum Mechanics: Pictures description

This is a question related to the Schrodinger and Heisenberg picture. Consider a physical system. There are two states- initial and final. Now this is the explanation from Schrodinger and Heisenberg ...
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### Time-evolution with a time-dependent Hamiltonian [closed]

Consider a quantum mechanical system whose Hilbert space of states is $\mathbb{C}^2$, and has Hamiltonian $$\hat{H}= \begin{pmatrix} E_0e^{t/w_0} & E_1 \\ E_1 & E_0e^{t/w_0} \end{pmatrix}$$ ...
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### How do I find the time evolution of a ket?

I have a question which reads: Let \begin{bmatrix} {E_0} & 0 & A \\ 0 & E_1 & 0 \\ A & 0 & E_0 \end{bmatrix} be the matrix representation of ...
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### Equivalent representations of stationary states in Quantum Mechanics

The time-dependent Schrodinger equation is given as $$i \hbar \frac{\mathrm d}{\mathrm dt}| \psi(t) \rangle = \hat{H} | \psi(t) \rangle.$$ To find how the states evolve in time we want to find the ...
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### Time evolution of operators, derivation

I don't understand something about the Heisenberg and interaction picture, in my notes the time evolution of operators for the Heisenberg and interaction picture is derived, by inserting them into the ...
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### Time-dependence in QM

When you have a system governed by some Hamiltonian H that starts in some state $\lvert a \rangle$, the way to calculate its time-dependence is to decompose into a linear combination of eigenstates of ...
### The $N$th-order identity of the time-ordered exponential in Quantum Mechanics
In Quantum Mechanics, one often defines the time ordered exponential like e.g. here. Now my question is how the factor of $N!$ arises. I know the simplex volume as the following integral: \begin{...