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In an attempt to regularize a previously known exactly solvable model [Yang and Zhang, Eur. J. Phys. textbf{40}, 035401 (2019)], we find yet another exactly solvable toy model. The interesting point is that while the Hamiltonian of the model is parameterized by a function $f(x)$ defined on $[0, infty )$, its spectrum depends only on the end values of $f$, i.e., $f(0)$ and $f(infty )$. This model can serve as a good exercise in quantum mechanics at the undergraduate level.
The eigenstates and eigenenergies of a toy model, which arose in idealizing a local quenched tight-binding model in a previous publication [Zhang and Yang, EPL 114, 60001 (2016)], are solved analytically. This enables us to study its dynamics in a di
This work analyzes the effects of cubic nonlinearities on certain resonant scattering anomalies associated with the dissolution of an embedded eigenvalue of a linear scattering system. These sharp peak-dip anomalies in the frequency domain are often
The grand partition function of a model of confined quarks is exactly calculated at arbitrary temperatures and quark chemical potentials. The model is inspired by a softly BRST-broken version of QCD and possesses a quark mass function compatible with
We introduce and study the adiabatic dynamics of free-fermion models subject to a local Lindblad bath and in the presence of a time-dependent Hamiltonian. The merit of these models is that they can be solved exactly, and will help us to study the int
We address the question whether observables of an exactly solvable model of electrons coupled to (optical) phonons relax into large time stationary state values and investigate if the asymptotic expectation values can be computed using a stationary d