Integration of operator differential equations.
Integration of operator differential equations.
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算子微分方程的积分。
DOI：
10.1103/physrevd.40.3504
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发表时间：
1989
期刊：
影响因子：
--
通讯作者：
Dunne
中科院分区：
文献类型：
--
作者：
Bender;Dunne
In a previous paper we introduced a method for obtaining exact solutions to the operator differential equations of quantum mechanics. In that paper we showed how to solve some simple quantum-mechanical models and we suggested that the method could be used to obtain exact solutions to the operator differential equations of more complicated models, such as the anharmonic oscillator whose Hamiltonian is {ital H}={1/2}{ital p}{sup 2}+ {1/4}q{sup 4}. In this paper we further sharpen the formalism and introduce the concept of a minimal solution. We then obtain the exact minimal solution to the operator differential equations arising from two different anharmonic-oscillator models whose Hamiltonians are {ital H}={1/2}{ital p}{sup 2}+{1/4}q{sup r4} and {ital H}={1/4}{ital p}{sup 4}+{1/4}q{sup 4}.
In a previous paper we introduced a method for obtaining exact solutions to the operator differential equations of quantum mechanics. In that paper we showed how to solve some simple quantum-mechanical models and we suggested that the method could be used to obtain exact solutions to the operator differential equations of more complicated models, such as the anharmonic oscillator whose Hamiltonian is {ital H}={1/2}{ital p}{sup 2}+ {1/4}q{sup 4}. In this paper we further sharpen the formalism and introduce the concept of a minimal solution. We then obtain the exact minimal solution to the operator differential equations arising from two different anharmonic-oscillator models whose Hamiltonians are {ital H}={1/2}{ital p}{sup 2}+{1/4}q{sup r4} and {ital H}={1/4}{ital p}{sup 4}+{1/4}q{sup 4}.