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Schrodinger equation

| 🗖 nosplit | ↑ parent "Non-relativistic quantum mechanics" | words: 555 | descendant words: 4k | descendants: 55
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Experiments explained:
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Experiments not explained: those that the Dirac equation explains like:
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To get some intuition on the equation on the consequences of the equation, have a look at:
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The easiest to understand case of the equation which you must have in mind initially that of the Schrodinger equation for a free one dimensional particle.
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Then, with that in mind, the general form of the Schrodinger equation is:
Equation 26. Schrodinger equation
where:
  • is the reduced Planck constant
  • is the wave function
  • is the time
  • is a linear operator called the Hamiltonian. It takes as input a function , and returns another function. This plays a role analogous to the Hamiltonian in classical mechanics: determining it determines what the physical system looks like, and how the system evolves in time, because we can just plug it into the equation and solve it. It basically encodes the total energy and forces of the system.
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The argument of could be anything, e.g.:
Note however that there is always a single magical time variable. This is needed in particular because there is a time partial derivative in the equation, so there must be a corresponding time variable in the function. This makes the equation explicitly non-relativistic.
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The general Schrodinger equation can be broken up into a trivial time-dependent and a time-independent Schrodinger equation by separation of variables. So in practice, all we need to solve is the slightly simpler time-independent Schrodinger equation, and the full equation comes out as a result.
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Ancestors

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