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- https://phys.libretexts.org/Learning_Objects/A_Physics_Formulary/Physics/10%3A_Quantum_PhysicsQuantum mechanics, atomic physics, Schrödinger and Dirac equations
- https://phys.libretexts.org/Bookshelves/Quantum_Mechanics/Quantum_Mechanics_III_(Chong)/04%3A_Identical_Particles/4.02%3A_Symmetric_and_Antisymmetric_StatesHence, Equation (???) is explicitly symmetric: \[\begin{align} \begin{aligned} \hat{P}_{12} \, |+\!z, A\,;\, -z, B\rangle &= \frac{1}{\sqrt{2}} \Big(|\!-\!z\rangle|B\rangle |\!+\!z\rangle|...Hence, Equation (???) is explicitly symmetric: ˆP12|+z,A;−z,B⟩=1√2(|−z⟩|B⟩|+z⟩|A⟩+|+z⟩|A⟩|−z⟩|B⟩)=|+z,A;−z,B⟩. Likewise, if there is a spin-down particle at A and a spin-up particle at B, the bosonic two-particle state is \[|-\!z, A\,;\, +z, B\rangle = \frac{1}{\sqrt{2}} \Big…
- https://phys.libretexts.org/Courses/Georgia_State_University/GSU-TM-Introductory_Physics_II_(1112)/zz%3A_Back_Matter/10%3A_13.1%3A_Appendix_J-_Physics_Formulas_(Wevers)/1.10%3A_Quantum_PhysicsQuantum mechanics, atomic physics, Schrödinger and Dirac equations
- https://phys.libretexts.org/Bookshelves/Nuclear_and_Particle_Physics/Nuclear_and_Particle_Physics_(Walet)/07%3A_Symmetries_and_Particle_Physics/7.04%3A_Discrete_SymmetriesLet us first look at the key discrete symmetries – parity P (space inversion) charge conjugation C and time-reversal T .
- https://phys.libretexts.org/Bookshelves/Quantum_Mechanics/Quantum_Mechanics_(Fowler)/03%3A_Mostly_1-D_Quantum_Mechanics/3.01%3A_1-D_Schrodinger_Equation_-_Example_SystemsRather, the lowest energy state must have the minimal amount of bending of the wavefunction necessary for it to be zero at both walls but nonzero in between -- this corresponds to half a period of a s...Rather, the lowest energy state must have the minimal amount of bending of the wavefunction necessary for it to be zero at both walls but nonzero in between -- this corresponds to half a period of a sine or cosine (depending on the choice of origin), these functions being the solutions of Schrödinger’s equation in the zero potential region between the walls.
- https://phys.libretexts.org/Bookshelves/Nuclear_and_Particle_Physics/Nuclear_and_Particle_Physics_(Walet)/03%3A_Nuclear_Masses/3.06%3A_Properties_of_Nuclear_StatesNuclei are quantum systems, and as such must be described by a quantum Hamiltonian. Fortunately nuclear energies are much smaller than masses, so that a description in terms of non-relativistic quantu...Nuclei are quantum systems, and as such must be described by a quantum Hamiltonian. Fortunately nuclear energies are much smaller than masses, so that a description in terms of non-relativistic quantum mechanics is possible. Such a description is not totally trivial since we have to deal with quantum systems containing many particles. Rather then solving such complicated systems, we often resort to models.
