A beutiful derivation of a formula for pi. At first, 1-1/3+1/5-1/7+1/9-.... seems unrelated to circles, but in fact there is a circle hiding here, as well as some interesting facts about prime numbers in the context of complex numbers.

A beutiful derivation of a formula for pi. At first, 1-1/3+1/5-1/7+1/9-.... seems unrelated to circles, but in fact there is a circle hiding here, as well as some interesting facts about prime numbers in the context of complex numbers.

In this video, we learn how to add, subtract, multiply, and divide complex numbers. In the dividing portion of this video (7:05), we look at how to use the complex conjugate to rewrite quotients.

In this representation I discuss the main principles of quantum mechanics behind the quantum computer. and How to build a device that can manipulate the energy operator of the Schrodinger Equation for an electron to change its spin...

In this video, the teacher explains how to multiply complex numbers using the double distributive property. They review the distributive property and the imaginary unit, emphasizing the importance of simplifying expressions involving i...

We've learned a bit about quantum mechanics from a strictly conceptual and qualitative standpoint. But now it's time to dig a little deeper. Quantum mechanics is mathematics, so if we want to understand it on a fundamental level, we have...

Particle-on-a-Ring Example #1: Calculate Electron Probability

Particle-on-a-Ring: Theory and Interpretation

Postulates of Quantum Mechanics: Expectation Values

Postulates of Quantum Mechanics: Orthogonality of Wavefunctions

Dividing complex numbers can be more complicated than multiplying complex numbers since when the result is a fraction, in order to write that fraction as a complex number in standard form, it must be separated into a real part plus an...

Postulates of Quantum Mechanics: Hermitian Operators 1

In the previous tutorial we introduced our second quantum problem, that of the quantum barrier potential. Again, this involves a free particle that encounters a barrier of finite potential. We've already solved the Schrödinger equation...

Proof of the steady state amplitude and phase for a spring mass damper system with an harmonic load acting on it.



Once you get good at it, you don't need to recreate another z equation like I've done. You can just solve as if...

In this video playlist I show you how to solve different math problems for Algebra, Geometry, Algebra 2 and Pre-Calculus. The video will provide you with math help using step by step instruction. Math help tutorials is just what you need...

In this video playlist you will learn everything you need to know with complex and imaginary numbers (3 - 2i)

👉 Learn how to write the equation of a polynomial when given imaginary zeros. Recall that a polynomial is an expression of the form ax^n + bx^(n-1) + . . . + k, where a, b, and k are constants and the exponents are positive integers. The...

👉 Learn how to write the equation of a polynomial when given complex zeros. Recall that a polynomial is an expression of the form ax^n + bx^(n-1) + . . . + k, where a, b, and k are constants and the exponents are positive integers. The...

👉 Learn how to write the equation of a polynomial when given complex zeros. Recall that a polynomial is an expression of the form ax^n + bx^(n-1) + . . . + k, where a, b, and k are constants and the exponents are positive integers. The...

Understanding complex numbers as zeros

Write the polynomial with complex zeros

We are beginning to get a glimpse of quantum mechanical principles from a rigorous, mathematical perspective. Now that we know how to use operators in conjunction with wavefunctions, let's get a better sense of what wavefunctions...

In this video playlist I show you how to solve different math problems for Algebra, Geometry, Algebra 2 and Pre-Calculus. The video will provide you with math help using step by step instruction. Math help tutorials is just what you need...

👉 Learn how to write the equation of a polynomial when given imaginary zeros. Recall that a polynomial is an expression of the form ax^n + bx^(n-1) + . . . + k, where a, b, and k are constants and the exponents are positive integers. The...