In the Copenhagen interpretation, which is what is typically taught to undergraduate students, particles are in superposition. What is superposition? In quantum mechanics, there is no equation that states...

Why do certain elements have similar properties? Because of the way electrons are arranged around the nucleus of atoms. But why are electrons arranged specifically in certain orbitals and shells? The structure of...

The many worlds interpretation of quantum mechanics was put forth by graduate student Hugh Everett in 1957. It was considered preposterous at the time, but is now going mainstream. It requires us to...

Physicists know how to use the equations of quantum mechanics to predict things, but don't really understand what is fundamentally going on.



The primary challenge is that according to the...

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Why Everything in the universe is a spring (kind of). Why everything is a spring. Classical springs like you might have in your mattress have a harmonic oscillation. And this behavior has a quantum...

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By the end of 1905, we had two big new equations in physics. Max Planck’s, Energy equals Planck’s constant times the frequency, and Einstein’s Energy equals the mass times the speed of light squared. A...

Five areas of physics worth remembering: Classical mechanics, energy and thermodynamics, electromagnetism, Relativity, and Quantum Mechanics. Classical mechanics - two main concepts worth knowing. The first is...

After learning calculus and linear algebra, it's time for differential equations! This is one of the most important topics in mathematics, especially for those who are interested in physics and engineering, as these equations show up...

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 part we build three quantum computers that can process simple commands by manipulating the Energy Operators in Schrodinger Equation. <br/>
Solving NOT gate by quantum computing, Solving Controlled NOT gate by quantum computing

We've talked about the Schrödinger equation before, but we really didn't dig into it with any depth at all. Now it's time to really get in there and do the math. What is the Hamiltonian operator? What is the time-independent Schrödinger...

Quantum Harmonic Oscillator: Calculating Zero-Point Energy and Energy Spacing

Now that we understand the Schrödinger equation, it's time to put it to good use, and solve a quantum problem. Let's find the eigenfunctions and eigenenergies associated with a quantum particle restricted to an infinite square well. This...

In this video, I calculate the energy and momentum for an electron in a quantized system (a porphyrin). ***Using the particle-on-a-ring model.

In this video we see how the Schrodinger equation comes out very simply from the conservation of energy. First. Throughout these 2 videos, I kept talking about predicting the future, and that if you know the present state, you can...

Postulates of Quantum Mechanics: Orthogonality of Wavefunctions

In the previous tutorial we solved the Schrödinger equation for a quantum particle in an infinite square well. This is also known as the problem of the particle in a box. But there is a lot to unpack regarding the results, enough to...

QM Applications: Particle-in-a-Box (Derivation)

Postulates of Quantum Mechanics: Eigenvalues & Eigenfunctions

In this video, we discuss the conceptual aspects of the quantum mechanics model, Particle-in-a-Box (also called the Infinite Potential Well model): Wavefunctions and Energy Eigenvalues. NEXT VIDEO: Particle-in-a-Box Example Problems

Now that we've covered the particle in a box, we are familiar with the concept of a quantum problem. Let's move on to our second quantum problem, that of the quantum barrier potential. With this one, we don't have an infinite square well...

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...

We just introduced the classical harmonic oscillator, so now let's look at the quantum version! Obviously this is much trickier, but let's solve the Schrödinger equation and see what the solution tells us about the quantum world.

Particle in a Finite Potential Well: Quantum Tunneling