Solving the von Neumann equation with time-dependent Hamiltonian. Part I: Method
نویسندگان
چکیده
The unitary operators U(t), describing the quantum time evolution of systems with a time-dependent Hamiltonian, can be constructed in an explicit manner using the method of time-dependent invariants. We clarify the role of Lie-algebraic techniques in this context and elaborate the theory for SU(2) and SU(1,1). We show that the constructions known as Magnus expansion and Wei-Norman expansion correspond with different representations of the rotation group. A simpler construction is obtained when representing rotations in terms of Euler angles. The many applications are postponed to Part II of the paper.
منابع مشابه
On the von Neumann equation with time-dependent Hamiltonian. Part II: Applications
This second part deals with applications of a general method to describe the quantum time evolution determined by a Schrödinger equation with time-dependent Hamiltonian. A new aspect of our approach is that we find all solutions starting from one special solution. The two main applications are reviewed, namely the Bloch equations and the harmonic oscillator with time-dependent frequency. Even i...
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