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  1. M

    Coupled Differential Equations

    Hi all, I want to solve equations of the form: \dot x + x + y = sin(\omega t) \dot y = \dot x - y This is not a standard type of form for Runge-Kutta or linear systems of equations because \dot y = f(\dot x, y, t) instead of \dot y = f(x, y, t). Any hints or links to place for...
  2. M

    Hydrodynamics Question

    If I have some water in a thin (on the order of micrometer or nanometer even) cylinder, a meniscus will form due to hydrodynamics and surface tension effects. There will be some characteristic height of the meniscus above the surface of the "bulk" water. Let's call this height "h". If I make...
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    What is a frustrated system?

    this term is often used when discussing spin glasses, etc.
  4. M

    Second Quantization and Field Operators

    back to the original question...i have been studying these things for the past few days and wrote a latex document on the subject. nothing really new here, but i tried to focus on pedagogy and examples so that someone with a basic knowledge of QM can understand 2nd quantization. take a look at...
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    Momentum to Energy Representation in 3D Box

    Consider a 3D particle in a square box. One can represent a complete set of quantum states by indexing them with their momentum component quantum numbers. So a state would be |p_x p_y p_z>. If one goes to the energy basis, two momentum states (say |1 0 0> and |0 1 0>) will correspond to the same...
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    Second Quantization and Field Operators

    When defining a field operator, textbooks usually say that one can define an operator which destroys (or creates) a particle at position r. What does this really mean? Are they actually referring to destroying (or creating) a state who has specific quantum numbers associated with the geometry...