By David Park

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**Extra resources for Introduction to the Quantum Theory**

**Sample text**

4). 12. Show, using Taylor’s series, that the frequency of light emitted in a transition out of a state whose energy is Wn is given by where Δn is the change in the quantum number n. 15) and state the conditions under which the second term can be neglected in discussing Bohr’s theory. 13. In the Bohr model, how fast is an electron in the nth circular orbit of hydrogen actually moving? 14. In an atom, the innermost electrons are not much affected by the outer ones. In the Bohr theory, how fast do the inner electrons of 92U travel?

Deeper than this, however, Newton was a thoroughgoing atomist, and it went against his instinct of the uniformity of nature to suppose that matter is one thing and light something entirely different. In this, as we shall see, he was perfectly right. The first contemporary suggestion of the discrete nature of light is found in the work of Max Planck and Albert Einstein around 1900. Although Planck did not really believe that the energy levels of an oscillator are discrete, he found that he could explain blackbody radiation if he counted them as if they were discrete.

The important idea here is that the discrete atomic energy states are analogous to the discrete overtones of a vibrating system such as a violin string or a column of air. This suggestion is the basis of our present understanding of stationary atomic states. ” In fact, it was reserved for others to do this, since de Broglie had not fully realized how the principle of superposition applies to matter waves. But he had discovered a new manifestation of the uniformity of nature, the universality of the relation between waves and particles, calling for a new form of dynamics, which should be to newtonian dynamics as wave optics is to geometrical optics.

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