Related Experiment Video
Updated: May 9, 2026

Generation and Coherent Control of Pulsed Quantum Frequency Combs
Published on: June 8, 2018
General coalescence conditions for the exact wave functions: higher-order relations for two-particle systems
Yusaku I Kurokawa1, Hiroyuki Nakashima, Hiroshi Nakatsuji
1Quantum Chemistry Research Institute, JST, CREST, Kyodai Katsura Venture Plaza 107, Goryo Oohara 1-36, Nishikyo-ku, Kyoto 615-8245, Japan.
Abstract:
We derived the necessary conditions that the non-relativistic time-independent exact wave functions for two-particle systems must satisfy at a coalescence (or cusp) point. Some of such necessary conditions are already known to be Kato's cusp condition (CC) and Rassolov and Chipman's CC. In the present study, we extended and generalized those conditions, calling them generalized coalescence conditions (GCCs). Kato's CC and Rassolov and Chipman's CC were shown to be specific cases included in the GCCs. The GCCs can be applied not only to Coulombic systems but also to any systems where the interaction between two particles is represented in a power series of the inter-particle distance. We confirmed the correctness of our derivation of these GCCs by applying the free complement wave functions of a hydrogen atom in ground and excited states, a harmonic oscillator, and a system with an interacting potential of V = r.
Related Concept Videos
Equilibrium Conditions for a Particle
To understand the concept of equilibrium, let us first consider the forces acting on an object. When different forces act on an object, they can...
¹H NMR: Long-Range Coupling
In alkenes, spin information is communicated via σ–π overlap, as seen in allylic (four-bond) and homoallylic (five-bond) couplings. These coupling interactions are stronger when the σ bond is parallel to the alkene π orbitals.
Molecular Orbital Theory II
First Law: Particles in Two-dimensional Equilibrium
Newton's first law tells us about the...
First Law: Particles in One-dimensional Equilibrium
Basic Postulates of Kinetic Molecular Theory: Particle Size, Energy, and Collision

