Note on operadic harmonic oscillator

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...

Comments on Vacuum Energy of Harmonic Oscillator

Unlike its classical counterpart, the ground state of a quantum harmonic oscillator yields a non-zero value which has led to a significant problem regarding the cosmological constant. We will show that since observables, including that of energy, serve as a reference frame for an observer, not only is the harmonic oscillator fluctuating at the ground level, so is the reference frame of the obse...