TY - JOUR

T1 - Why are complex numbers needed in quantum mechanics?

T2 - Some answers for the introductory level

AU - Avelar Sotomaior Karam, Ricardo

PY - 2020

Y1 - 2020

N2 - Complex numbers are broadly used in physics, normally as a calculation tool that makes things easier due to Euler's formula. In the end, it is only the real component that has physical meaning or the two parts (real and imaginary) are treated separately as real quantities. However, the situation seems to be different in quantum mechanics, since the imaginary unit i appears explicitly in its fundamental equations. From a learning perspective, this can create some challenges to newcomers. In this article, four conceptually different justifications for the use/need of complex numbers in quantum mechanics are presented and some pedagogical implications are discussed.

AB - Complex numbers are broadly used in physics, normally as a calculation tool that makes things easier due to Euler's formula. In the end, it is only the real component that has physical meaning or the two parts (real and imaginary) are treated separately as real quantities. However, the situation seems to be different in quantum mechanics, since the imaginary unit i appears explicitly in its fundamental equations. From a learning perspective, this can create some challenges to newcomers. In this article, four conceptually different justifications for the use/need of complex numbers in quantum mechanics are presented and some pedagogical implications are discussed.

U2 - 10.1119/10.0000258

DO - 10.1119/10.0000258

M3 - Journal article

VL - 88

SP - 39

EP - 45

JO - American Journal of Physics

JF - American Journal of Physics

SN - 0002-9505

IS - 1

ER -