Abstract
The wave-particle duality asserting that everything possesses partly wave and partly particle properties is presented. This duality, on which Quantum Mechanics is based, provides the required kinetic energy to counterbalance the attractive nature of the interactions and stabilizes both the microscopic and the macroscopic structures of matter. The core of Quantum Mechanics can be condensed to the following three fundamental principles possessing amazing quantitative predictive power: Those of Heisenberg, Pauli, and Schrödinger.
So reasonable the incomprehensible.
O. Elytis
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Notes
- 1.
The magnitude of k is related to the wavelength λ through the relation, k = 2π/λ, and its direction gives the direction of propagation of the wave.
- 2.
- 3.
Δx is the so-called standard deviation defined by the relation: \( \Updelta x^{2} \equiv \,\left \langle {\left( {x - \langle x \rangle } \right)^{2} } \right\rangle \, = \,\left\langle {x^{2} } \right\rangle - \left\langle x \right\rangle^{2} . \) A similar definition applies to Δp x with x replaced by p x The symbol \( \langle f \rangle \), for any quantity f, denotes its average value.
- 4.
Although the average value of p x can be zero, if the contributions of positive and negative values cancel each other.
- 5.
By using the symmetry of the sphere and by assuming uniform density for any value of r.
- 6.
The correct relativistic relation between kinetic energy and momentum is \( \varepsilon_{k} = \left( {m_{o}^{2} c^{4} + c^{2} p^{2} } \right)^{1/2} - m_{o} c^{2} \). In the non-relativistic limit, \( m_{o} c^{2} \gg c\,p, \) becomes \( \varepsilon_{k} \approx p^{2} /2m_{o} , \) while in the extreme relativistic limit, \( m_{o} c^{2} \ll c\,p \), becomes ε k  = cp, where m o is the rest mass of the particle.
- 7.
For the numerical values of all universal constants see Table 1 in p. 141.
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© 2011 Eleftherios N. Economou
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Economou, E.N. (2011). The Wave-Particle Duality. In: A Short Journey from Quarks to the Universe. SpringerBriefs in Physics, vol 1. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-20089-2_3
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DOI: https://doi.org/10.1007/978-3-642-20089-2_3
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