Imaginary and Complex Numbers

Neither of equations (iii) or (iv) are solutions to equation (7.46). However, if n was such that n2 was negative, then both functions would be solutions to the equation. This would require us to define the square root of a negative number, which is at odds with our understanding of what constitutes a real number. In Chapter 2, Volume 2, we extend the concept of the number to include so-called imaginary and complex numbers, which embrace the idea that the square root of a negative number can be defined. 

Before we go into the mathematical framework behind wave mechanics, we will review one more mathematical concept normally seen in high school imaginary and complex numbers. As discussed in Section 1.2, for a general quadratic equation ax2 + bx+c =... 

This chapter introduces imaginary and complex numbers as a legitimate extension of the number system. The key points discussed in this chapter include ... 

Our principal boundary condition is that the solution be real, because imaginary and complex numbers cannot represent physically measurable quantities like the position of the oscillator. From the trigonometric identity in Eq. (2.93) we can write... 

Variables and Units handle real, imaginary, and complex numbers with or without associated units. A high-performance calculation engine provides speed and sophisticated memory management to help find solutions faster. 

Imaginary and complex numbers cannot be used to represent any physically measurable quantity, but are useful in quantum mechanics, since wave functions can be imaginary or complex. 

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