Table of Contents
- 1 Why do we use complex numbers in quantum mechanics?
- 2 How are complex numbers different from vectors?
- 3 What are complex numbers give four examples & discuss if those numbers are purely real or complex?
- 4 Does quantum mechanics use real numbers or complex numbers?
- 5 What is the difference between complex numbers and reals?
Why do we use complex numbers in quantum mechanics?
The main reason why complex numbers show up in quantum mechanics is because they make linear algebra much easier.
How are complex numbers different from vectors?
Complex Numbers as Vectors Complex numbers behave exactly like two dimensional vectors. Indeed real numbers are one dimensional vectors (on a line) and complex numbers are two dimensional vectors (in a plane). There are no three dimensional or higher dimensional numbers obeying all the rules of elementary algebra.
Do you need complex numbers for quantum mechanics?
Complex numbers, i.e., numbers with a real and an imaginary part, are essential for mathematical analysis, while their role in other subjects, such as electromagnetism or special relativity, is far less fundamental.
What are complex numbers give four examples & discuss if those numbers are purely real or complex?
Complex numbers are the numbers that are expressed in the form of a+ib where, a,b are real numbers and ‘i’ is an imaginary number called “iota”. The value of i = (√-1)….Examples.
Complex Number | Real Number | Imaginary Number |
---|---|---|
7-9i | 7 | -9i |
-6i | 0 | -6i (Purely Imaginary) |
6 | 6 | 0i (Purely Real) |
Does quantum mechanics use real numbers or complex numbers?
Quantum mechanics uses both complex and real numbers. (And there’s more to that than just saying that real numbers are a subset of complex numbers 🙂 ). One of the facets of the predictions of Quantum Mechanics is that there are discrete states (or answers to the QM equations) for things like the energy or momentum states of systems.
Why do we use complex numbers in physics?
In classical physics (and especially the study of waves) complex numbers are used because, via the complex exponential, they allow easy handling of sinusoidal functions. Thus we have phasors and the like. But the key rule for such applications is that only the real part is taken for the actual quantity.
What is the difference between complex numbers and reals?
Now, the main difference between the complex numbers and the reals is that the complex numbers are algebraically closed. What this means is that any polynomial with coefficients in the complex numbers splits into linear factors.