Abstract
Quantum mechanics is the centerpiece of modern physics. Teaching quantum mechanics have been difficult because of complex numbers, Hilbert space, and interpretations. We show that a real formulation of quantum mechanics without complex numbers and Hilbert space is included in Schrödinger’s 1926 papers. The legitimacy and advantages of such a real formulation were justified in 1960s. High-caliber quantum mechanics textbooks in real formulation existed since 1970s in France. Experimental observations of atomic and molecular wavefunctions using scanning tunneling microscopy necessitates a real formulation. Practically, in chemical physics and condensed-matter physics, real wavefunctions are sufficient, especially regarding to density-functional theory (DFT). Outlined here is a freshman-sophomore course of real quantum mechanics covering a wide range of applications to dispense with complex numbers and Hilbert space. As shown, the derivation of the real Schrödinger equations is transparent, the mathematics is elementary, and the interpretation is intuitive.
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