Inverted Oscillator

Abstract

The inverted harmonic oscillator problem is investigated quantum mechanically. The exact wave function for the confined inverted oscillator is obtained and it is shown that the associated energy eigenvalues are discrete and it is given as a linear function of the quantum number $n$.

4 pages

References in corpus (8)

• The Phase of the Riemann Zeta Function and the Inverted Harmonic Oscillator
• Quantum Mechanics of Damped Systems II. Damping and Parabolic Potential Barrier
• Fingerprints of Classical Instability in Open Quantum Dynamics
• Quantum states of a generalized time-dependent inverted harmonic oscillator
• Operator Methods of the Parabolic Potential Barrier
• The decay of quantum D-branes
• Statistical fluctuations for the fission process on its decent from saddle to scission
• Tachyon Backgrounds in 2D String Theory

Cited by in corpus (29)

• Theory of strain in single-layer transition metal dichalcogenides
• Physics of the Inverted Harmonic Oscillator: From the lowest Landau level to event horizons
• Quasinormal Modes and Hawking-Unruh effect in Quantum Hall Systems: Lessons from Black Hole Phenomena
• Optimized sympathetic cooling of atomic mixtures via fast adiabatic strategies
• Factorization method and new potentials from the inverted oscillator
• Squeezing and robustness of frictionless cooling strategies
• Equivalence between free quantum particles and those in harmonic potentials and its application to instantaneous changes
• Stochastic Bohmian mechanics within the Schrödinger-Langevin framework: A trajectory analysis of wave-packet dynamics in a fluctuative-dissipative medium
• Ehrenfest Dynamics and Frictionless Cooling Methods
• Quantum chaos associated with emergent ergosurface in transition layer between type-I and type-II Weyl semimetals
• Dynamical scaling symmetry and asymptotic quantum correlations for time-dependent scalar fields
• Self-Accelerating Matter Waves
• Fast Frictionless Expansion of an Optical Lattice
• Quantum inverted harmonic potential
• Quantum confinement in 1D systems through an imaginary-time evolution method
• Ehrenfest approach to open double-well dynamics
• Four-mode squeezed states in de Sitter space: A study with two field interacting quantum system
• Duality between the quantum inverted harmonic oscillator and inverse square potentials
• Self-acceleration in non-Hermitian Systems
• Self-accelerating Parabolic Cylinder Waves in 1-D
• Exact solution of the position-dependent mass Schrödinger equation with the completely positive oscillator-shaped quantum well potential
• Non-Hermitian inverted Harmonic Oscillator-Type Hamiltonians Generated from Supersymmetry with Reflections
• Polynomial Heisenberg algebras and Painlevé equations
• Free to Harmonic Unitary Transformations in Quantum and Koopman Dynamics
• Time-dependent quantum geometric tensor and some applications
• A unifying mechanical equation with applications to non-holonomic constraints and dissipative phenomena
• Parametric Competition in non-autonomous Hamiltonian Systems
• Fresh look at the effects of gravitational tidal forces on a freely-falling quantum particle
• On the diagonalization of quadratic Hamiltonians