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Chapter 27
Chapter 27

... would be emitted when a quantized oscillator jumped from one energy level to the next lower one ...
Kvantfysik Lecture Notes No. 4x
Kvantfysik Lecture Notes No. 4x

... figure). The particle then has angular momentum pointing in the ẑ direction given by Lz = pR = `h̄. Hence, the angular momentum is also quantized, and in fact comes in integer multiples of h̄. We will call ` the angular momentum quantum number. In a later lecture we will show more precisely how the ...
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... The Rutherford-Bohr model of the atom described the electron orbiting around the nucleus in circular orbits. This is a planetary model like the planets orbiting the Sun. However, in terms of Quantum Mechanics the electron has to be regarded as a wave so that experimental observations agree with theo ...
Systematic improvement of the correlation energy of solids
Systematic improvement of the correlation energy of solids

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Particle in a box



In quantum mechanics, the particle in a box model (also known as the infinite potential well or the infinite square well) describes a particle free to move in a small space surrounded by impenetrable barriers. The model is mainly used as a hypothetical example to illustrate the differences between classical and quantum systems. In classical systems, for example a ball trapped inside a large box, the particle can move at any speed within the box and it is no more likely to be found at one position than another. However, when the well becomes very narrow (on the scale of a few nanometers), quantum effects become important. The particle may only occupy certain positive energy levels. Likewise, it can never have zero energy, meaning that the particle can never ""sit still"". Additionally, it is more likely to be found at certain positions than at others, depending on its energy level. The particle may never be detected at certain positions, known as spatial nodes.The particle in a box model provides one of the very few problems in quantum mechanics which can be solved analytically, without approximations. This means that the observable properties of the particle (such as its energy and position) are related to the mass of the particle and the width of the well by simple mathematical expressions. Due to its simplicity, the model allows insight into quantum effects without the need for complicated mathematics. It is one of the first quantum mechanics problems taught in undergraduate physics courses, and it is commonly used as an approximation for more complicated quantum systems.
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