# What is Non-hermitian: Definition and 13 Discussions

Non-Hermitian quantum mechanics is the study of quantum-mechanical Hamiltonians that are not Hermitian. Notably, they appear in the study of dissipative systems. Also, non-Hermitian Hamiltonians with unbroken parity-time (PT) symmetry have all real eigenvalues.

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1. ### I Simulation of non-Hermitian quantum mechanics

I noticed the research on NHQM in the following news release. New physics rules tested on quantum computer Published: 19.2.2021 Information for relevant paper is provided as follows. Quantum simulation of parity–time symmetry breaking with a superconducting quantum processor Shruti Dogra...
2. ### I Non-Hermitian wavefunctions and their solutions

I was wondering if anyone has worked with non-Hermitian wavefunctions, and know of an approach to derive real and trivial values for their observables using numerical calculations? Cheers
3. ### A Non-selfadjointness and solutions

Hi, I have the two operators: $$Q = i\hbar \frac{d}{dx} - \gamma$$$$Q' = -i\hbar \frac{d}{dx} - \gamma$$ where ##\gamma## is a constant. Both of these are not self-adjoint, as they do not follow the condition: ...
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### I Relationship between a non-Hermitian Hamiltonian and its solution

Hello, I Have a non-Hermitian Hamiltonian, which is defined as an ill-condition numbered complex matrix, with non-orthogonal elements and linearily independent vectors spanning an open subspace. However, when accurate initial conditions are given to the ODE of the Hamiltoanian, it appears to...
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### A How does a pseudo-Hermitian model differ from a Hermitian?

Hi, I have not been able to learn how a pseudo-Hermitian differs from a Hermitian model. If one has a hermitian model that satisfies all the fundamental prescriptions of quantum mechanics, a non-Hermitian would not, as it yields averages with complex values. How does a pseudo-Hermitian differ...
6. ### B Non-Hermitian operator for superposition

It is said that no Hermitian operator gives a time evolution where "I observed the spin to be both up and down" is a possible result. If you use non-Hermitian operator.. then it's possible.. and what operator is that where it is possible in principle where "I observed the spin to be both up and...
7. ### Probability for a non-hermitian hamiltonian

Homework Statement Given a non-hermitian hamiltonian with V = (Re)V -i(Im)V. By deriving the conservation of probability, it can be shown that the total probability of finding a system/particle decreases exponentially as e(-2*ImV*t)/ħ Homework Equations Schrodinger Eqn, conservation of...
8. ### Finding Eigenvectors and Values of Non-Hermitian Matrices with Mathematica

Hey, I have two quick questions, Does mathematica automatically find the eigenvectors and values when you find the eigensystem of a non-Hermitian matrix? I've been searching the net trying to find a way to find these vectors/values but everything I find briefly touches upon...
9. ### Diagonalize a non-hermitian matrix

I'm learning "the transformation optics" and the first document about this method is "Photonic band structures" ( Pendry, J. B. 1993). In this document, the transfer matrix T is non-hermitian, Ri and Li are the right and left eigenvectors respectively. Pendry defined a unitary matrix...
10. ### Simultaneous diagonalisation of non-hermitian operator (Bloch theorem)

A valuable math result for quantum mechanics is that if two hermitian operators (physical observables) commute, then a simultaneous basis of eigenvectors exists. Nevertheless, there are cases in which two operators commute without being both hermitians -- a really common one is when one operator...
11. ### Exploring Non-Hermitian Hamiltonians for Particle Decay and Quasi-Bound States

Can someone explain how non-Hermitian Hamiltonians are used to account for particle decay?
12. ### Proof that (p + ix) operator is non-hermitian (easy)

theres one line that keeps coming up in proofs that I don't get. How do i get from \int (\hat{p}\Psi1)*\Psi2 + i \int (\hat{x}\Psi1)\Psi2 to \int ( (\hat{p}-i\hat{x}) \Psi1)*\Psi2 using the fact that p and x are Hermitian. im sure its painfully simple but i can't see it.
13. ### Help with expected value of non-hermitian operators

I know that with an Hermitian operator the expectation value can be found by calculating the (relative) probabilities of each eigenvalue: square modulus of the projection of the state-vector along the corresponding eigenvector. The normalization of these values give the absolute probabilities...