Quantum Theory
Quantum Theory
Quantum theory is very strange. The mathematics makes use of abstractions that have no physical representation. The equations do accurately describe quantum phenomenon. Don’t try and interpret them, it can’t be done!
Quantum theory has to be a good approximation to what is really happening. Whatever that is is beyond our current understanding.
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Some definitions are required.
Dirac or Bra-ket notation
The Dirac notation takes the form \(<f|\vec{v}>\).
A ket \(|\vec{v}>\) is a vector \(\vec{v} \in V\).
A bra \(<f|\) is a function that maps a vector to a complex number \(f:V \rightarrow \mathbb{C}\).
Planck Constant
The Planck Constant \(h\) has a fixed numerical value in SI units \(6.626 070 15 \cdot 10^{-34} J\cdot s\). A photon of frequency \(f\) has energy \(E = hf\).
In quantum theory, frequencies are often expressed as radians per second. A full cycle is \(2\pi\) radians, so the reduced Planck Constant \(\hbar = h/2\pi\) is often used.
Bohr Magneton
The Bohr Magneton \(\mu_B\) is a unit of magnetic moment of an electron. Magnetic moments are often given in terms of the Borh Magneton.
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\(e\) is the electron charge
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\(m_e\) is the electron mass