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**Complex Schrodinger Equation, references??**

hopefully i can explain what i am looking for well enough for somebody to understand. I am interested in finding any references for work that has been done on solving the schrodinger equation in C^n rather than in R^n, as in on the complex plane with complex valued argument rather than the real case which is what we normally consider when doing quantum mechanics. Obviously i understand that a particle's probability to be located at the position (1 + i) is not exactly physically understandable. But nonetheless, I am interested in what work has been done on the schrodinger equation in the complex plane and am hoping that somebody will be able to provide some references and/or ideas about the subject. (Also there will be major problems with any sort of normalization, but nonetheless i'm interested. )

I have tried minimal searching with google scholar and my universities article search but have not been able to find any references. Thank you for any input or help, i appreciate it greatly.