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Stationary states and time
Stationary states and time

... If E were the whole of the energy of the particle (as it would be if it were a free particle, unaffected by its surroundings) then this eigenvalue equation is H f(x) = E f(x) where H is the Hamiltonian operator for the system, H   ...
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Matt`s talk about our observation of quantum
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... Pupil Well, clearly, if the error on either EB or EA were bigger than the gap EA − EB between them, we would not be able to tell whether they were different or not. Maybe I could put it another way: if the net error (whatever that means!) on the two measurements is bigger than EA −EB , I could not t ...
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... Solution to WAVE EQUATION gives set of mathematical expressions called E. Schrodinger ...
Chapter 5: Electrons in Atoms
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appendix 3 - University of Sydney
appendix 3 - University of Sydney

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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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