Basics of the Quantum Oscillation

Nobuhiro Shimizu, T. Morooka, Mititada Morisue

In this paper we propose a new measurement method to investigate the basic properties of a Josephson relaxation oscillator (RO) using dc superconducting quantum interference devices (SQUIDs). The dc SQUIDs linearly and continuously convert the oscillating current into voltage enabling the waveforms to be clearly observed. The voltage and current waveforms have been measured simultaneously. The basic operation of the RO has been experimentally confirmed.

F. Suekane

Xiao-Chun Gao, Jing‐Bo Xu, Tiezheng Qian +1 more

Taking the generalized time-dependent harmonic oscillator (GTHO) and singular time-dependent harmonic oscillator (STHO) as illustrative examples, we discuss the connection between the quantum basic invariants and classical Noether's theorem and, for the system, find: (1) The classical basic invariants and general form of classical invariants. (2) The current algebra and corresponding operator algebra. (3) A kind of converse of the Noether's theorem. (4) The connection between the so-called symmetry algebra ({ G k } algebra) and the classical current algebra through the operator algebra.

V. Grecchi

This paper is a continuation of the previous one: "Quantum mechanics: some basic techniques for some basic models, I: The models".The main subject is the perturbation theory in quantum mechanics giving diverging perturbation series for the energy levels of the oscillators.Thus, a short historical introduction on the methods of the sum of diverging power series is given.

Shigemi Araki