Bicomplex Quantum Mechanics: II. The Hilbert Space
Dominic Rochon, Sebastien Tremblay
Abstract
Using the bicomplex numbers T which is a commutative ring with zero divisors defined by T=\w0 + w1 i1 + w2 i2 + w3 j | w0, w1, w2, w3 ∈ R\ where i12 = -1, i22 = -1, j2 = 1, i1 i2 = j = i2 i1, we construct hyperbolic and bicomplex Hilbert spaces. Linear functionals and dual spaces are considered and properties of linear operators are obtained; in particular it is established that the eigenvalues of a bicomplex self-adjoint operator are in the set of hyperbolic numbers.
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