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An Introductory Review of Quantum Mechanics
Published in Ramaswamy Jagannathan, Sameen Ahmed Khan, Quantum Mechanics of Charged Particle Beam Optics, 2019
Ramaswamy Jagannathan, Sameen Ahmed Khan
The existence of a nonzero ground state energy, so-called zero-point energy, can be understood intuitively in terms of the uncertainty principle. As seen in (3.363), the ground state wave function is a Gaussian with a finite width. It is not localized means that the position of the oscillating particle is fluctuating around the equilibrium even in the ground state unlike the classical oscillator which will be at rest in the equilibrium position in the ground state. As a consequence of this uncertainty in position, say Δx, there will be a finite uncertainty in the momentum of the particle, ~ℏ/Δx, as dictated by the Heisenberg uncertainty principle. This intrinsic ground state motion implies the existence of a minimum energy.
Z
Published in Splinter Robert, Illustrated Encyclopedia of Applied and Engineering Physics, 2017
[atomic, nuclear] The lowest energy of a system under quantum mechanical conditions. Under the uncertainty principle, even a single particle out by itself in the outer space does not have zero kinetic energy; based on the definitions of the uncertainty principle, the particle will have zero-point energy. Alternatively, at the absolute zero temperature, 0.0000000000000000 K, theoretically there will be no motion and hence no discernable energy content, although the particle does exist and hence it has (quantum-mechanical) probabilities associated with it, as well as motion of the nuclei and orbiting electrons. The latter makes the case purely theoretical, with no physical means of achieving the true absolute zero Kelvin. Under zero-point energy conditions, electromagnetic radiation is still allowed. This electromagnetic energy density can reach excessive values, theoretically up to 1058 J/m3 (see Figure Z.11).
Symbols, Terminology, and Nomenclature
Published in W. M. Haynes, David R. Lide, Thomas J. Bruno, CRC Handbook of Chemistry and Physics, 2016
W. M. Haynes, David R. Lide, Thomas J. Bruno
Zeeman effect - The splitting of an energy level of an atom or molecule, and hence a splitting of spectral lines arising from that level, as a result of the application of an external magnetic field. Zener diode - A control device utilizing a p-n junction with a well defined reverse-bias avalanche breakdown voltage. Zeotrope - A liquid mixture that shows no maximum or minimum when vapor pressure is plotted against composition at constant temperature. See Azeotrope. Zero-point energy - The energy possessed by a quantum mechanical system as a result of the uncertainty principle even when it is in its lowest energy state; e.g., the difference between the lowest energy level of a harmonic oscillator and the minimum in the potential well. Zeta potential () - The electric potential at the surface of a colloidal particle relative to the potential in the bulk medium at a long distance. Also called electrokinetic potential. Zwitterions - Neutral compounds having formal unit electrical charges of opposite sign. Some chemists restrict the term to compounds with the charges on non-adjacent atoms. Sometimes referred to as inner salts, dipolar ions (a misnomer). [5]
Evaluation of structure-reactivity correlation of efficient corrosion inhibitor ionic liquids for mild steel in acidic medium
Published in Journal of Dispersion Science and Technology, 2023
Ashish Rathore, Shobhana Sharma, Ankit Sharma, Sushil Kumar Sharma
The various thermochemical parameters of imidazolium cation-based ionic liquid in the gas phase were calculated by the B3LYP/6-31G method of DFT, as shown in Table 6. Zero point energy exhibits the lowest possible energy of the quantum mechanical system. The analysis of thermochemical estimations like thermal Enthalpies and Gibbs free energy reveals the spontaneous and exothermic nature of the synthetic methodology of ionic liquids. The reduction in entropy and degree of freedom during the preparation of inhibitors demonstrate the negative value of entropy. The polarization increases with dipole moment, further enhancing the solubility of inhibitors in polar solvents.[28] Thus, in the present article, IL-2 inhibitors possess more dipole moment value and higher solubility, improving the number of molecules in solution and adsorption phenomena. This causes an increase in surface coverage (θ) and enhances the inhibition efficiency of this inhibitor.