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A remark on the integration of Schrödinger equation using quantum Itô's formula

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Abstract

When the potential is the Fourier transform of a totally finite complex-valued measure, a formula for the one-parameter unitary group generated by the Schrödinger operator in L 2 (IRn) is obtained entirely in terms of the basic field operators in a suitable Fock space by means of quantum stochastic calculus.

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References

  1. Combe, P., Hoegh-Krohn, R., Sirigue, M., and Sirigue-Collins, M., ‘Generalised Poisson Processes in Quantum Mechanics and Field Theory’, Phys. Rep. 77, No. 3, 1981 (New Stochastic Methods in Physics (C. Dewitte-Morette and K.D. Elworthy, eds.), North-Holland, Amsterdam).

  2. Hudson, R.L. and Parthasarathy, K.R., ‘Quantum Itô's Formula and Stochastic Evolution’, submitted to Comm. Math. Phys.

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  1. Indian Statistical Institute, Delhi Centre, 110016, New Delhi, India

    K. R. Parthasarathy

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  1. K. R. Parthasarathy
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Parthasarathy, K.R. A remark on the integration of Schrödinger equation using quantum Itô's formula. Lett Math Phys 8, 227–232 (1984). https://doi.org/10.1007/BF00402238

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  • DOI: https://doi.org/10.1007/BF00402238

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