Hi there. I had this question going around in my mind for a long time. Basically, I wanted to know if there is a need for the use of the complex field for the wave functions in quantum mechanics, or if quantum mechanics can be built with real wave functions, instead of working in the complex field and the use of the complex field is only driven as a mathematical facility.(adsbygoogle = window.adsbygoogle || []).push({});

As many here know, the physical states in quantum mechanics are described by generalized vectors in Hilbert space, this generalized vectors are complex functions, and the modulus of this complex functions give the probability distribution for the particle position, momentum, etc. The complex wave functions give the facility to work with the 'wave' aspects found in quantum mechanics (they provide the facility to account for the interference terms, destructive and constructive interference, etc). My question is if all of this mathematical facilities provided by the use of the complex field can be recovered by using only real functions instead of complex functions, and if not, which is the root for the need of the complex field in quantum mechanics.

Similarly, one can work in wave classical mechanics with complex functions, by writting the sines and cosines by means of complex exponentials. But then one take the real or imaginary parts to get at the end a real function, wich discribes the process in the real world. In quantum mechanics the wave functions are always complex, but the physical predictions are given by the probabilities distributions, related to the modulus of this wave functions, and such modulus are ofcourse always real.

Thanks in advance for your answers,

Regards.

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# Quantum Mechanics in the real field

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