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    • 15.5: Relativistic Quantum Mechanics
      https://phys.libretexts.org/Bookshelves/Quantum_Mechanics/Quantum_Physics_(Ackland)/15%3A_The_Quantum_Mechanics_Nobody_Rreally_Understands/15.05%3A_Relativistic_Quantum_Mechanics
      \[\begin {align*} \hat{H}^{2} \psi(\mathbf{r}, t) & = \left\{ c^{2} \left[ \left(\alpha_{x} \right)^{2} \left(\hat{p}_{x} \right)^{2}+ \left(\alpha_{y} \right)^{2} \left(\hat{p}_{y} \right)^{2}+ \left...\[\begin {align*} \hat{H}^{2} \psi(\mathbf{r}, t) & = \left\{ c^{2} \left[ \left(\alpha_{x} \right)^{2} \left(\hat{p}_{x} \right)^{2}+ \left(\alpha_{y} \right)^{2} \left(\hat{p}_{y} \right)^{2}+ \left(\alpha_{z} \right)^{2} \left(\hat{p}_{z} \right)^{2} \right]+m^{2} c^{4} \beta^{2} \right\} \psi(\mathbf{r}, t) \\& +c^{2} \left\{ \left(\alpha_{x} \alpha_{y}+\alpha_{y} \alpha_{x} \right) \hat{p}_{x} \hat{p}_{y}+ \left(\alpha_{y} \alpha_{z}+\alpha_{z} \alpha_{y} \right) \hat{p}_{y} \hat{p}_{z}+ \…
    • 13.3: Free Particles and the de Broglie Wavelength
      https://phys.libretexts.org/Bookshelves/Quantum_Mechanics/Advanced_Quantum_Mechanics_(Kok)/13%3A_The_Schrodinger_Equation/13.3%3A_Free_Particles_and_the_de_Broglie_Wavelength
      The value λ that shows up in these equations is the wavelength; that is it’s the range of x over which it takes the sine or the cosine to go through one complete cycle. The fact that the...The value λ that shows up in these equations is the wavelength; that is it’s the range of x over which it takes the sine or the cosine to go through one complete cycle. The fact that the wave function, this abstract mathematical object which is used to figure out things about the state of a particle, also shows interference effects is what we mean when we say that sometimes particles behave like waves.

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