By Breit G.

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Extra resources for An Interpretation of Diracs Theory of the Electron

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This model considers the waveforms that would result from a disturbance of a sphere that is covered with water. 8) where φ is the amplitude function and v is the phase velocity of the wave. 9) 24 Chapter 2 The Quantum Mechanical Way of Doing Things where ν is the frequency. 10) and the relationship between the frequency and the wavelength of a transverse wave, distance × time−1 = v (distance/time) , allow us to write ν 2 = m2 v 4 / h2 . 11) 2 4 ∂ 2φ 2 m v = −4π φ. 12) Therefore, we find that Substituting this in the general equation above, we obtain ∂ 2φ ∂ 2φ ∂ 2φ + 2 + 2 = ∂x 2 ∂y ∂z 1 ν2 −4π 2 v 4 m2 h2 φ.

We will have more to say about orthogonal wave functions in later chapters. 2 The Wave Equation It was shown in 1924 by de Broglie that a moving particle has a wave character. That idea was demonstrated in 1927 by Davisson and Germer when an electron beam was diffracted by a nickel crystal. Even before that experimental verification, Erwin Schrödinger adapted the wave model to the problem of the hydrogen atom. In that case, the model needs to describe a three-dimensional wave. Classical physics had dealt with such models in a problem known as the flooded planet problem.

Although they have some applicability to real problems, such models are most useful in illustrating the methods of formulating problems and applying quantum mechanical procedures. As a result, almost every introductory book on quantum mechanics includes discussion on particles in boxes. 1 The Particle in a One-Dimensional Box In this model, we treat the behavior of a particle that is confined to motion in a box. The box is taken to be one dimensional for simplicity although a three-dimensional problem is not much more difficult, and we will take up that problem next.

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