# How do I create a Quantum Time Operator with DifferentialEquations?

**URL:** <https://discourse.julialang.org/t/how-do-i-create-a-quantum-time-operator-with-differentialequations/65766>\
**Category:** Quantum\
**Created:** [August 4, 2021, 12:47am UTC](https://discourse.julialang.org/t/how-do-i-create-a-quantum-time-operator-with-differentialequations/65766 "2021-08-04T00:47:26Z")\
**Posts on this page:** 1\
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**Author:** ![jagot](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/jagot/32/12217_2.png) [@jagot](https://discourse.julialang.org/u/jagot)\
**Post date:** [August 5, 2021, 8:22am UTC](https://discourse.julialang.org/t/how-do-i-create-a-quantum-time-operator-with-differentialequations/65766/3 "2021-08-05T08:22:46Z")

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Chris is right about Magnus propagators being the method of choice for QM. See also this earlier post: [How to efficiently exponentiate a complex (symmetric) tridiagonal matrix?](https://discourse.julialang.org/t/how-to-efficiently-exponentiate-a-complex-symmetric-tridiagonal-matrix/56982)

Are you sure you want this Hamiltonian matrix though?

> [@Noel\_Araujo](#):
>
> `H = [1 1;-1 1]./sqrt(2)`

This is non-Hermitian, which is very untypical in Markovian (=normal) QM.

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