Crypto-unitary forms of quantum evolution operators

Abstract

For the description of quantum evolution, the use of a manifestly time-dependent quantum Hamiltonian $\mathfrak{h}(t)={\mathfrak{h}}^{†}(t)$ is shown equivalent to the work with its simplified, time-independent alternative $G\ne G^{†}$. A tradeoff analysis is performed recommending the latter option. The physical unitarity requirement is shown fulfilled in a suitable ad hoc representation of Hilbert space.

15 pp

References in corpus (13)

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Cited by in corpus (14)

• Non-Hermitian interaction representation and its use in relativistic quantum mechanics
• Time-Dependent Pseudo-Hermitian Hamiltonians and a Hidden Geometric Aspect of Quantum Mechanics
• The problem of coexistence of several non-Hermitian observables in PT-symmetric quantum mechanics
• Non-Hermitian Heisenberg representation
• Non-Hermitian coupled cluster method for non-stationary systems and its interaction-picture reinterpretation
• Some results on the dynamics and transition probabilities for non self-adjoint hamiltonians
• Wheeler-DeWitt equation and the applicability of crypto-Hermitian interaction representation in quantum cosmology
• Hybrid form of quantum theory with non-Hermitian Hamiltonians
• Pseudo-invariant approach for a particle in a complex time-dependent linear potential
• Discrete-coordinate crypto-Hermitian quantum system controlled by time-dependent Robin boundary conditions
• Hermitian--to--quasi-Hermitian quantum phase transitions
• Quantum control and the challenge of non-Hermitian model-building
• Non-stationary quantum mechanics in hybrid non-Hermitian interaction representation
• Consistent treatment of quantum systems with a time-dependent Hilbert space