Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

American Journal of Physics

Continuity conditions on Schrödinger wave functions at discontinuities of the potential

David Branson

Published Nov 1, 1979• 14 citations
Publisher

Abstract

Several standard arguments which attempt to show that the wave function and its derivative must be continuous across jump discontinuities of the potential are reviewed and their defects discusssed. Three arguments which it is hoped are more satisfactory are then presented.
DOI
10.1119/1.11688

Related papers

Continuity of Wave-function and Its First Rank Differential

Fang Jing-huai

According to mathematical principles the article rigidly deduces from Schrodinger equation the continuity conditions of wave-function and its first rank differential.They will continue if potential function continues,or if it doesn't continue but has a bound in the contiguity of the discontinuous point.However,the continuity of wave-function and its first rank differential will be uncertain if potential function is discontinuous,and boundless in the contiguity of the discontinuous point.

Journal of Nantong University•Jan 1, 2007•0 citations

There are no quantum jumps, nor are there particles!

H. D. Zeh

Abstract: Quantum theory does not require the existence of discontinuities: neither in time (quantum jumps), nor in space (particles), nor in spacetime (quantum events). These apparent discontinuities are readily described objectively by the continuous process of decoherence occurring locally on a very short time scale according to the Schrdinger equation for interacting systems, while the observerÕs Ôincrease of informationÕ is appropriately represented by the resulting dynamical decoupling of the corresponding components of the global wave function. Physics Letters A172, 189 (1993) 2As far as is known, all properties of closed quantum systems are perfectly described by means of wave functions in configuration space (in general, wave functionals of certain fields) dynamically evolving smoothly according to the time-dependent Schrdinger equation. However, the condition of being closed (or shielded against interactions with the environment) can easily be estimated to be quite exceptional. It characterizes very special (usually atomic) systems from which the laws of quantum mechanics were derived. When the shielding ceases, most notably during measurements, discontinuous

Physics Letters B•Jan 1, 1992•1 citation

Discontinuity in the first derivative of the Schrödinger wave function

Dipankar Home, S. Sengupta

Bound state problems in quantum mechanics are considered for the edge of a square well potential and singular points of a Coulomb and a δ-function potential. (AIP)

American Journal of Physics•Jun 1, 1982•7 citations

Three Issues of The Quantum Mechanics

Zhao Xinjun

The paper discusses three issues, the first order derivative of wave function is not continuous if potential has a infinite observable, and the 5 function normalization of the eigenfunction with continuous eigenvalue, and the introduction of the zero value condition of the wave function. The first two issues are not detailed demonstrated and the third not rationally treated in current literature.

Journal of Xingjiang Normal University•Jan 1, 2003•0 citations

Continuity on First Derivative of Wave Function

Zhu Yu-xia

Continuity on first derivative of wave function is discussed by means of several instances of finite and infinite transitions of potential function and hereby continuity conditions is pinpointed. 

Journal of Lianyungang Technical College•Jan 1, 2002•0 citations

New boundary conditions in tunneling

Antonio Boulhosa Nassar, José Maria Filardo Bassalo, P. T. S. Alencar +3 more

Via the hydrodynamical formulation of quantum mechanics, we propose new boundary conditions to the problem of tunneling through sharp-edged potential barriers with and without dissipation. Above all, these boundary conditions can be matched without assuming continuity of the wave function at a surface σ where the potential undergoes a finite jump. Our approach yields a general expression for transmission probability from which tunneling with and without dissipation can be directly correlated to standard discussions found in textbooks.

Il Nuovo Cimento B•Apr 1, 2004•0 citations
Abstract: Quantum theory does not require the existence of discontinuities: neither in time (quantum jumps), nor in space (particles), nor in spacetime (quantum events). These apparent discontinuities are readily described objectively by the continuous process of decoherence occurring locally on a very short time scale according to the Schrdinger equation for interacting systems, while the observerÕs Ôincrease of informationÕ is appropriately represented by the resulting dynamical decoupling of the corresponding components of the global wave function. Physics Letters A172, 189 (1993) 2As far as is known, all properties of closed quantum systems are perfectly described by means of wave functions in configuration space (in general, wave functionals of certain fields) dynamically evolving smoothly according to the time-dependent Schrdinger equation. However, the condition of being closed (or shielded against interactions with the environment) can easily be estimated to be quite exceptional. It characterizes very special (usually atomic) systems from which the laws of quantum mechanics were derived. When the shielding ceases, most notably during measurements, discontinuous
Via the hydrodynamical formulation of quantum mechanics, we propose new boundary conditions to the problem of tunneling through sharp-edged potential barriers with and without dissipation. Above all, these boundary conditions can be matched without assuming continuity of the wave function at a surface σ where the potential undergoes a finite jump. Our approach yields a general expression for transmission probability from which tunneling with and without dissipation can be directly correlated to standard discussions found in textbooks.