Fe b 20 07 Quantum Mechanics with Complex Time : A Comment to the Paper

In (quant–ph/0701141) Rajeev studied quantization of the damped simple harmonic oscillator and introduced a complex–valued Hamiltonian (which is normal). In this note we point out that the quantization is interpreted as a quantum mechanics with complex time. We also present a problem on quantization of classical control systems. In the paper [1] Rajeev studied a quantization of the damped simple harmonic oscillator and introduced a complex–valued Hamiltonian (which is normal). In the case where dissipative systems are treated complex–valued Hamiltonians cannot be avoided in general. In this note we point out that the quantization with complex–valued Hamiltonian is interpreted as a quantum mechanics with complex time, which is in a certain sense reasonable. Anyway, quantization of dissipative systems must be widely studied. Quantum Mechanics with Complex Hamiltonian ∗E-mail address : [email protected]