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Quantum Mechanics

The path integral formulation is a fundamental approach within the broader framework of quantum mechanics, describing the behavior of quantum systems.
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The statement of the theorem

The Path Integral Formulation provides an alternative representation for the quantum mechanical propagator K(xb,tb;xa,ta)K(x_b, t_b; x_a, t_a), which satisfies the Schrödinger equation: \n∂K∂tb=iℏH^K\frac{\partial K}{\partial t_b} = \frac{i}{\hbar} \hat{H} K \nIn the path integral approach, this evolution is given by the functional integral over the Hamiltonian HH: \nK(xb,tb;xa,ta)=∫Dx(t)eiℏS[x(t)]K(x_b, t_b; x_a, t_a) = \int \mathcal{D}x(t) e^{\frac{i}{\hbar} S[x(t)]}