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The Schrödinger equation is a linear differential equation, meaning that if two state vectors | and | are solutions, then so is any linear combination | = | + | of the two state vectors where a and b are any complex numbers.
When the Schrödinger Equation is combined with a quantum description of the electromagnetic field, a theory known as quantum electrodynamics, the result is one of the most accurate theories of matter that has ever been put forth. Keeping this in mind, let us forge ahead in our discussion of the quantum universe and how to apply quantum theory ...
Feb 8, 2013 · We obtain the Schrödinger equation from a mathematical identity by a slight generalization of the formulation of classical statistical mechanics based on the Hamilton–Jacobi equation.
- Born Interpretation
- Copenhagen Interpretation
- Other Interpretations
There are many philosophical interpretations of the wave function, and a few of the leading ideas will be considered here. The main idea, called the Born probability interpretation (named after physicist Max Born) comes from the simple idea that the wave function is square integrable; i.e. This rather simple formula has great physical implications....
An extension of the above ideas can be made. Since the Born interpretation says that the actual position particle cannot be known, we can derive the following. If Ψ 1 , Ψ 2 , Ψ 3 , … Ψ n {\displaystyle \Psi _{1},\Psi _{2},\Psi _{3},\dots \Psi _{n}} are solutions to the wave equation, then the superposition of those solutions, i.e. is also a solutio...
There are various other interpretations, such as the many-worlds interpretation, and quantum determinism.
Jun 1, 2014 · We show how the highly accurate and efficient Constant Perturbation (CP) technique for steady-state Schrödinger problems can be used in the solution of time-dependent Schrödinger problems with explicitly time-dependent Hamiltonians, following a technique suggested by Ixaru (2010).
- V. Ledoux, M. Van Daele
- 2014
3 days ago · Ab-initio variational wave functions for the time-dependent many-electron Schrödinger equation ... A significant amount of effort has been devoted to developing scalable and accurate techniques ...
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Apr 27, 2020 · While ML methods are now accepted as high accuracy approaches to construct interatomic potentials for applications, the use of ML to solve the Schrödinger equation, either vibrational or electronic, while not new, is only now making significant headway towards applications.
