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Thread: some question about path integral

  1. #1 some question about path integral 
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    I want to know what problems we need path integral to solve, Idonot think it's very different from the normal quantum mechanics.
    And what is the Heisenberg picture
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  2. #2  
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    Hi zbnju, welcome to the forum. When you do QM you have a choice to make: the Hamiltonian route or the Lagrangian route . The latter leads to the path integral formulation and the former to the more usual formulation of the state vector. The two are really quite different. The first treats time very differently to position, the second is much more compatible with spacetime as a single entity so is currently favoured in theories that try to reconcile General Relativity with Quantum mechanics.

    The Heisenberg picture has time dependence in the operator rather than the state vector, whereas in the Schroedinger picture the operators are constant and the states evolve in time. They are equivalent to each other.
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  3. #3  
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    Quote Originally Posted by Jilan View Post
    Hi zbnju, welcome to the forum. When you do QM you have a choice to make: the Hamiltonian route or the Lagrangian route.
    I just got my hands on an article that was published in the American Journal of Physics called Nine formulations of quantum mechanics. You might want to read it. It's online at http://math.bu.edu/people/mak/Styer%...hys%202002.pdf
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  4. #4  
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    thank you, but I still feel confused.
    The Hamiltonian and the Lagrangian usually can transform to each other, the book also get the expression of the path integral through the state vector,aren't they equal?
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  5. #5  
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    They are equivalent, so you should be able to get on from the other. You don't need a state vector in the path integral approach.
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