Bicomplex Quantum Mechanics: II. The Hilbert Space
نویسندگان
چکیده
Using the bicomplex numbers T which is a commutative ring with zero divisors defined by T = {w0+w1i1+w2i2+ w3j | w0, w1, w2, w3 ∈ R} where i21 = −1, i22 = −1, j = 1, i1i2 = j = i2i1, we construct hyperbolic and bicomplex Hilbert spaces. Linear functionals and dual spaces are considered on these spaces and properties of linear operators are obtain; in particular it is established that the eigenvalues of a bicomplex self-adjoint operator are in the set of hyperbolic numbers. E-mail: [email protected] E-mail: [email protected]
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