约翰·雅各布·巴耳末Johann Jakob Balmer

巴耳末的父亲也叫约翰·雅各布·巴耳末，是一位首席法官。巴耳末的母亲是Elizabeth Rolle 巴耳末。巴耳末是他父母儿子中的长子。他在利斯塔尔上了第一所学校，这个镇刚刚成为巴塞尔乡村半州的首府。然后，为了接受中等教育，他在巴塞尔的一所学校学习，在那里他的数学成绩优异，并决定在大学学习这门学科。

为了在大学学习数学，巴耳末先后就读于卡尔斯鲁厄大学和柏林大学。他的学习课程最终导致他于1849年从巴塞尔大学获得博士学位，学位论文是关于摆线的。
巴耳末一生都在巴塞尔教书。从1859年到1898年去世，他一直是该市一所女子中学的数学教师。从1865年到1890年，他还兼任巴塞尔大学的数学讲师，其主要兴趣领域是几何学。他于1868年43岁时与Christine Pauline Rinck结婚，他们有六个孩子。

然而，尽管巴耳末一生都是数学教师和讲师，他最为人所铭记的是他在光谱系方面的工作，以及他在1885年给出的氢原子光谱线波长的公式。这一点只写在他关于元素光谱的两篇论文之一中，第二篇写于1897年。令人惊讶的是，巴耳末写出使他闻名的关于氢原子光谱线的论文时已经六十岁，而写出他关于这一主题的唯一另一篇著作时已经七十二岁。但如果不是因为他在一个实质上属于物理学的问题上的工作，巴耳末在数学史上今天会不为人知，因为尽管几何学是他一生感兴趣的主题，他却没有对几何学做出特别重要的贡献。

然而，巴耳末做出的主要贡献更多地依赖于他的数学技能，而不是他对物理学的理解，因为他提出了一个公式，给出了氢原子产生的观测谱线的波长，而没有给出任何物理解释。巴耳末的著名公式是$\lambda = \Large\frac {hm^2 }{m^2 - n^2 }$。代入$n = 2$和$h = 3654.6 \times 10^{-8}$ cm，该公式对$m$ = 3, 4, 5, 6给出的波长精确度很高。以前的尝试寻找的是完全不同类型的公式，未能得出任何与实验证据相符的结果。代入$m = 7$，巴耳末得到了下一条谱线的预测值，事实上，巴塞尔大学的一位同事能够告诉巴耳末，这条谱线已被观测到，其波长与巴耳末的公式预测的波长高度精确地一致。

在1885年的论文中，巴耳末提出，给$n$赋予其他小整数值将给出氢原子产生的其他谱线的波长。事实上，这一预测被证明是正确的，这些谱线系后来被观测到。该公式成立的原因在巴耳末有生之年未被理解，直到1913年尼尔斯·玻尔的理论工作才得以解释。

巴耳末的公式引出了其他原子光谱线的更一般公式。其他基于巴耳末的思想而能够取得此类结果的人包括约翰内斯·里德伯、Kayser和卡尔·龙格。

Johann Balmer's father was also named Johann Jakob Balmer and he was a Chief Justice. Johann's mother was Elizabeth Rolle Balmer. Johann was the eldest of his parents sons. He attended his first school in Liestal, a town which had just become the capital of the half canton of Basel-Landschaft. Then, for his secondary education, he studied at a school in Basel where he excelled in mathematics and decided to study that topic at university.

For his university studies in mathematics Balmer attended the University of Karlsruhe and the University of Berlin. His course of studies led to a doctorate which he received from the University of Basel in 1849 for a dissertation on the cycloid.
Balmer taught in Basel all his life. From 1859 until his death in 1898 he was a school teacher of mathematics at a secondary school for girls in the city. From 1865 until 1890 he was also a university lecturer in mathematics at the University of Basel where his main field of interest was geometry. He married Christine Pauline Rinck in 1868 when he was 43 years old and they had six children.

However, despite being a mathematics teacher and lecturer all his life, Balmer is best remembered for his work on spectral series and his formula, given in 1885, for the wavelengths of the spectral lines of the hydrogen atom. This was set out in one of only two papers which he wrote on spectra of the elements, the second being in 1897. It is surprising to realise that Balmer was sixty years old when he wrote the paper for which he is famous on the spectral lines of the hydrogen atom and that he was seventy-two when he wrote his only other work on this topic. But for his work on what amounts to a problem in physics, Balmer would be unknown today within the history of mathematics since he made no contribution to geometry of special significance despite it being the topic of interest throughout his life.

The major contribution which Balmer made, however, depended much more on his mathematical skills than on his understanding of physics, for he produced a formula which gave the wavelengths of the observed lines produced by the hydrogen atom without giving any physical explanation. Balmer's famous formula is

In his paper of 1885 Balmer suggested that giving $n$ other small integer values would give the wavelengths of other series produced by the hydrogen atom. Indeed this prediction turned out to be correct and these series of lines were later observed. The reason why the formula holds was not understood in Balmer's lifetime and had to wait until the theoretical work of Niels Bohr in 1913.

Balmer's formula led to more general formulae for the spectral lines of other atoms. Others who, basing their ideas on those of Balmer, were able to achieve such results included Rydberg, Kayser and Runge.