On Harmonic Oscillator Representation Using Small Value of the Oscillator Length

Harmonic Oscillator

Quantum Harmonic Oscillator Sonification

This work deals with the sonification of a quantum mechanical system and the processes that occur as a result of its quantum mechanical nature and interactions with other systems. The quantum harmonic oscillator is not only regarded as a system with sonifiable characteristics but also as a storage medium for quantum information. By representing sound information quantum mechanically and storing...

Generalized Spiked Harmonic Oscillator

A variational and perturbative treatment is provided for a family of generalized spiked harmonic oscillator Hamiltonians H = − d dx + Bx + A x + λ xα ,where B > 0, A ≥ 0 , and α and λ denote two real positive parameters. The method makes use of the function space spanned by the solutions |n> of Schrödinger’s equation for the potential V (x) = Bx + A x . Compact closed-form expressions are obtai...

Optional Problems on the Harmonic Oscillator

â φα = αφα , with α a complex number (see next page for a discussion of â and â†). Such a state is called a “coherent state”. Coherent states turn out to be the closest quantum analog of classical states with well-defined amplitudes and phases, and are extremely important in e.g. the quantum mechanical description of laser light, radio cavities, Bose-Einstein condensates, and just about everyth...

Kraus representation of a damped harmonic oscillator and its application

Yu-xi Liu, Șahin K. Özdemir, Adam Miranowicz, and Nobuyuki Imoto The Graduate University for Advanced Studies (SOKENDAI), Shonan Village, Hayama, Kanagawa 240-0193, Japan Frontier Research System, The Institute of Physical and Chemical Research (RIKEN), Wako-shi 351-0198, Japan SORST Research Team for Interacting Career Electronics, Hayama, Kanagawa 240-0193, Japan CREST Research Team for Photo...