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Lecture Notes: Condensed Matter Theory I (TKM1)
Lecture Notes: Condensed Matter Theory I (TKM1)

... The ground state of a Bose gas is clearly di¤erent. At T = 0 all bosons occupy the state with lowest energy, which is in our case p = 0. An interesting question is then whether this macroscopic occupation of one single state remains at small but …nite temperatures. Here, a macroscopic occupation of ...
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... In a cyclic process in which the system does net work on its surroundings, it is observed to be physically necessary not only that heat be taken into the system, but also, importantly, that some heat leave the system. The difference is the heat converted by the cycle into work. In each repetition o ...
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... was what really triggered the birth of antimatter, because the equation is mainly based on squares and as we know for each square there are a positive and a negative square root. So, Dirac reasoned that the possibility of an electron with positive energy would be the same as one with negative energy ...
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... - in this case capitalized letters are used - a superscript number before the letter indicates the multiplicity of the state, i.e. the number of possibilities to combine the total L and total S to a total angular momentum J - for L > S the total momentum ranges from L - S to L + S, i.e. the multipli ...
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... direction. If the atoms passing through have angular momentum of   1 so L  2 but the z-component Lz  m is unknown, how many possibilities are there for deflection? A. 0 B. 1 C. 2 D. 3 E. Infinite ...
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SU(3) Model Description of Be Isotopes

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Quantum walk as a generalized measuring device
Quantum walk as a generalized measuring device

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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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