Category Archives: Quantum Mechanics

Constellation (TV series) and Many-Worlds Interpretation

There is a new TV series titled Constellation on Apple TV+. The plot so far (I don’t intend to be a spoiler and I don’t actually know much about the plot either because there have been only three episodes) is … Continue reading

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Square Root of Klein-Gordon

Replacing $E$ and $p$ by $i\hbar\frac{\partial}{\partial t}$ and $-i\hbar\nabla$, respectively, in the energy-momentum relation $$E^2=p^2c^2+m_0^2c^4$$ we obtain the Klein-Gordon operator $$\square=\frac{m_0^2c^2}{\hbar^2},$$ where $$\square=-\frac{1}{c^2}\frac{\partial^2}{\partial t^2}+\nabla^2$$ $\square$ is called the d’Alembertian or the wave operator. This time, replacing $E$ and $p$ by … Continue reading

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Real Structure, Fundamental Symmetry and Quantum Mechanics

In the standard Hermitian quantum mechanics, the space of states of a quantum mechanical system forms a complex Hilbert space in general. But often the space of states becomes a real vector space. When the space of states is a … Continue reading

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Doing Quantum Physics with Split-Complex Numbers

Theory of Photons (Electromagnetism) and Wave-Particle Duality of Light Earlier investigations on the nature of light show that, light must be described by electromagnetic waves or by particles (wave-particle duality). de Broglie hypothesized that what is true for photons should … Continue reading

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