Quantum Mechanics 012 : Schrodinger's equation

The 12th video tutorial in this introduction to quantum mechanics, covering Erwin Schrodinger's wave equation for a particle in 1 dimension and in a 3 dimensional potential energy field of an atom

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Science & Technology

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• physics
• academy

[nickharvey7]

I have read that the Planck constant is combined with pi so often that they came up with a new symbol hbar. I feel we lose part of the geometry by not having pi in the equation. So much of this is squared could this be because pi is the ratio of a circle’s circumference?

[physicsacademy]

I see it more as a mathematical convenience. It emerges due to the fact that we represent an oscillation as motion around a circle. k = 2 pi / wavelength and w = 2 pi / t so that when we treat the wavelength as a de Broglie wavelength we see that the particles' momentum is equal to ((h / 2 pi)*(2 pi / (h / p)). hbar, therefore, keeps pi in the equation and by doing so allows us to use complex numbers. This is also just a convenience in classical physics but necessary in quantum mechanics

[nickharvey7]

Nice video!

This is an invitation to see an artist theory on the physics of light and time!

This theory is based on two postulates

1. Is that the quantum wave particle function Ψ represents the forward passage of time ∆E ∆t ≥ h/2π itself

2. Is that Heisenberg’s Uncertainty Principle ∆×∆p×≥h/4π that is formed by the w- function is the same uncertainty we have with any future event that we can interact with turning the possible into the actual!

[nickharvey7]

@physicsacademy Thanks! I see this more as picture and therefore geometry because I am not much good at mathematics. I take it everything is squared because that is the physical nature of a wave. We have energy equals mass times the square of the speed of light so if must be something fundamental. It’s not just in Schrödinger’s equation.