Chinese Physics C > 1979, Vol. 3 > Issue(4): 511-517

APPROXIMATE SEQUENCE FORU（t,t₀）-OPERATOR

LI ZI-PING

Sinkiang University

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Abstract：
We give an approximate sequence for U（ t, t ₀）-operator.We prove the follow-ing theorems:Theorem 1.If the norm || H（ t）|| of H（ t）in equation（2.1）is a Lebesgue in-tegrable function with respect to t,then there is an approximate sequence{ U _n},such that for any state vector | Φ〉,| Ψ〉,the sequence < Φ| U _1^|Ψ>< Φ| U₂ ^_|Ψ>，......，< Φ| U_n ^_|Ψ>，......is uniform convergent with respect to t.Theorem 2.If in finite time interval,the norm || H（ t）|| of H（ t）in equation （2.1）is a Lebesgue integrable function,then equation（2.1）has unique solution.

References

[1]	P .W. Lanhoff, S. T. Epstein, M. Karplus, Rev. Mod. Phys., 44 (1972), 602.[2] C. L. Hammer and T. A. Weber, J. Math, Phys., 6 (1965), 1591.[3] 朱洪元，量子场论，科学出版社，(1960), 184页.[4] M. Reed. B. Simon, Method of modern mathematical Physics, 1 (1972), 216.

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LI ZI-PING. APPROXIMATE SEQUENCE FOR U（ t, t ₀）-OPERATOR[J]. Chinese Physics C, 1979, 3(4): 511-517.

LI ZI-PING. APPROXIMATE SEQUENCE FOR U（ t, t ₀）-OPERATOR[J]. Chinese Physics C, 1979, 3(4): 511-517. shu

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Received: 1978-04-23
Revised: 1900-01-01

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沈阳化工大学材料科学与工程学院沈阳 110142

APPROXIMATE SEQUENCE FORU（t,t₀）-OPERATOR

LI ZI-PING

Sinkiang University

Received Date:1978-04-23
Accepted Date:1900-01-01
Available Online:1979-08-05

Abstract:We give an approximate sequence forU（t,t₀）-operator.We prove the follow-ing theorems:Theorem 1.If the norm ||H（t）|| ofH（t）in equation（2.1）is a Lebesgue in-tegrable function with respect to t,then there is an approximate sequence{U_n},such that for any state vector |Φ〉,|Ψ〉,the sequence <Φ|U_1^|Ψ><Φ|U₂^_|Ψ>，......，<Φ|U_n^_|Ψ>，......is uniform convergent with respect tot.Theorem 2.If in finite time interval,the norm ||H（t）|| ofH（t）in equation （2.1）is a Lebesgue integrable function,then equation（2.1）has unique solution.