70 citations · 150 across the 9 of their papers we have counts for
9 papers
Explicit representations of Pollaczek polynomials corresponding to an exactly solvable discretisation of hydrogen radial Schrödinger equation
M. Aunola
We consider an exactly solvable discretisation of the radial Schrödinger equation of the hydrogen atom with l=0. We first examine direct solutions of the finite difference equation…
Connecting Berry's phase and the pumped charge in a Cooper pair pump
M. Aunola, J. J. Toppari
The properties of the tunnelling-charging Hamiltonian of a Cooper pair pump are well understood in the regime of weak and intermediate Josephson coupling, i.e. when $E_{\mathrm{J}}…
Exact, explicit and entire solutions to a nontrivial finite-difference equation and their applications
M. Aunola
Below, the explicit solution to a certain finite-difference equation is given and the required steps for derivation of these results are outlined. Everything is included as Mathema…
The discretised harmonic oscillator: Mathieu functions and a new class of generalised Hermite polynomials
M. Aunola
We present a general, asymptotical solution for the discretised harmonic oscillator. The corresponding Schrödinger equation is canonically conjugate to the Mathieu differential equ…
Tunnelling-charging Hamiltonian of a Cooper pair pump at large E_J\lesssim E_C: Modified Hamiltonians and renormalisability
M. Aunola
The properties of the tunnelling-charging Hamiltonian of a Cooper pair pump are well understood in the regime of weak and intermediate Josephson coupling, i.e. E_J\lesssim E_C. Ins…
Superconducting single-electron transistor and the phi-modulation of supercurrent
M. Aunola
An analytical expression for the supercurrent of a superconducting single-electron transistor (SSET) is derived. The derivation is based on analogy between the model Hamiltonian fo…