Coulomb Wave Function Calculator
Free online coulomb wave function calculator. Enter your values and get instant results with the formula, step-by-step working, a worked example and FAQs — everything runs locally in your browser on Calcton, no signup required.
中文版：库仑波函数在线计算器
库仑波函数 F₀(η, ρ) 是带电粒子在长程库仑势中的 s 波径向波函数，满足 u″ = (2η/ρ − 1)u：α 衰变（Gamow 理论）、核反应截面、卢瑟福散射的量子化描述都从它出发。η 大于 0 代表斥力，波函数在原点被压低 e^(−πη) 倍——这就是伽莫夫位垒穿透因子的来源。
实现：RK4 从 ρ = 1e-5 起步（初值 F ≈ C₀ρ、F′ ≈ C₀，步长 1e-4）把方程积分到目标 ρ；C₀(η) 用闭式 √(2πη/(e^(2πη)−1))（η = 0 时取 1 避免 0/0）。三重校验：η = 0 时三个 ρ 处与 sin ρ 一致（方程退化为球 Bessel）、C₀(1) 与权威值一致、斥力位垒区 F₀(1,1) 的量级与 e^(2√(2η)) 放大分析吻合。
参考值
F₀(0, 1) = sin 1 = 0.8414709848078965，F₀(0, π/2) = 1
C₀(1) = 0.1084225131020726（斥力把原点振幅压低一个量级）
F₀(1, 1) = 0.2275216605280774，F₀(0.5, 5) = −0.4904503333076388
How to use the Coulomb Wave Function Calculator
- Fill in the inputs with your own numbers — every field shows what it expects.
- The result updates instantly as you type; no "Calculate" click needed.
- Read the result card for the main figure, the step-by-step formula, and practical notes.
Frequently asked questions
Is the Coulomb Wave Function Calculator free?
Yes — all math calculators on Calcton are free, with no sign-up required. Your inputs are processed in your browser and never sent to a server.
Is there a Chinese version of this tool?
Yes. Use the Chinese version link above — it is the same calculator with the interface in Simplified Chinese.
References
Formulas and benchmarks used by this calculator follow these published sources.
KevinContent LeadCalcton Editorial Team · Last updated 2026-09-28
Kevin maintains Calcton's formula verification and content: every calculator cites the standard it implements, worked examples are recomputed programmatically, and health benchmarks follow WHO and international guidelines.
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