1990/08/01 by G. Barton, A. J. Bray, Alan J. McKane +1 · 2 citations
Physics and Astronomy · #Bound state #Classical mechanics #Energy (signal processing) #Ground state #Harmonic #Harmonic oscillator #Hydrogen atom #Master equation #Mathematical physics #Physics #Quantum #Quantum Mechanics and Applications #Quantum Mechanics and Non-Hermitian Physics #Quantum mechanics #Quantum, superfluid, helium dynamics #Schrödinger equation #Simple (philosophy) #Simple harmonic motion
paper · doi:10.1119/1.16402
openalex publication_date 1990/08/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/02
Change in the energy of bound states of the one-dimensional Schrödinger equation is investigated when distant boundaries are introduced where previously none existed. The argument covers the truly one-dimensional equation and, also, the radial equation for central potentials with spherically symmetric boundaries. A simple, explicit formula for this energy change is derived and is illustrated with specific examples, including the harmonic oscillator and the ground state of the hydrogen atom.