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11.6: Schrödinger's Equation
https://eng.libretexts.org/Bookshelves/Electrical_Engineering/Electro-Optics/Direct_Energy_(Mitofsky)/11%3A_Calculus_of_Variations/11.06%3A_Schr%C3%B6dinger's_Equation
The probability of finding an electron, for example, in a particular energy state is specified by $|\psi|^2$ where $\psi$ is called the wave function [136]. The quantum mechanical Hamiltonian \(H_...The probability of finding an electron, for example, in a particular energy state is specified by $|\psi|^2$ where $\psi$ is called the wave function [136]. The quantum mechanical Hamiltonian $H_{QM}$ is then the sum of the kinetic energy $E_{kinetic}$ and potential energy $E_{potential\, energy}$ . Using the of momentum definition of Equation $\ref{11.6.4}$ and the vector identity of Equation 1.6.8, we can rewrite the Hamiltonian.
11.5: Capacitor Inductor Example
https://eng.libretexts.org/Bookshelves/Electrical_Engineering/Electro-Optics/Direct_Energy_(Mitofsky)/11%3A_Calculus_of_Variations/11.05%3A_Capacitor_Inductor_Example
The Hamiltonian is the sum of the energy in the capacitor and the energy in the inductor. However, here to illustrate the use of the calculus of variations formalism, we write expressions for both the...The Hamiltonian is the sum of the energy in the capacitor and the energy in the inductor. However, here to illustrate the use of the calculus of variations formalism, we write expressions for both the total energy and the Lagrangian in terms of the specified variables: $t$ , $Q$ , and $\frac{dQ}{dt}$ . Solutions depend on initial conditions such as the charge stored in the capacitor and the current in the inductor at the initial time.
1.6: Electromagnetic Waves
https://eng.libretexts.org/Bookshelves/Electrical_Engineering/Electro-Optics/Direct_Energy_(Mitofsky)/01%3A_Introduction/1.06%3A_Electromagnetic_Waves
A uniform parallel plate capacitor with cross sectional area of plates $A =l \cdot w$ and distance between plates $d_{thick}$ , is shown on the left part of Figure $\PageIndex{1}$ , and it has cap...A uniform parallel plate capacitor with cross sectional area of plates $A =l \cdot w$ and distance between plates $d_{thick}$ , is shown on the left part of Figure $\PageIndex{1}$ , and it has capacitance $C =\frac{\epsilon A}{d_{thick}} \nonumber$ where $\epsilon$ is the permittivity of the insulator between the plates.
5.3: Quantum Hall Effect
https://eng.libretexts.org/Bookshelves/Electrical_Engineering/Electro-Optics/Direct_Energy_(Mitofsky)/05%3A_Hall_Effect/5.03%3A_Quantum_Hall_Effect
Around a hundred years after the discovery of the Hall effect, the quantum Hall effect was discovered. Klaus von Klitzing discovered the integer quantum Hall effect in 1980 and won the physics Nobel p...Around a hundred years after the discovery of the Hall effect, the quantum Hall effect was discovered. Klaus von Klitzing discovered the integer quantum Hall effect in 1980 and won the physics Nobel prize for it in 1985.
Front Matter
https://eng.libretexts.org/Bookshelves/Electrical_Engineering/Electro-Optics/Direct_Energy_(Mitofsky)/00%3A_Front_Matter
13.5: From Thomas-Fermi Theory to Density Functional Theory
https://eng.libretexts.org/Bookshelves/Electrical_Engineering/Electro-Optics/Direct_Energy_(Mitofsky)/13%3A_Thomas-Fermi_Analysis/13.05%3A_From_Thomas_Fermi_Theory_to_Density_Functional_Theory
The Thomas-Fermi method is the simplest ab initio solution of the calculation of the charge density and energy of electrons in an atom. Since no experimental data is used, the results of the calculati...The Thomas-Fermi method is the simplest ab initio solution of the calculation of the charge density and energy of electrons in an atom. Since no experimental data is used, the results of the calculation can be compared to experimental data from spectroscopic experiments to verify the results.
13: Thomas-Fermi Analysis
https://eng.libretexts.org/Bookshelves/Electrical_Engineering/Electro-Optics/Direct_Energy_(Mitofsky)/13%3A_Thomas-Fermi_Analysis
1.3: Conservation of Energy
https://eng.libretexts.org/Bookshelves/Electrical_Engineering/Electro-Optics/Direct_Energy_(Mitofsky)/01%3A_Introduction/1.03%3A_Conservation_of_Energy
For example, kinetic energy of a moving ball can be converted to heat by friction, or it can be converted to potential energy if the ball rolls up a hill. For example, if we say that an energy convers...For example, kinetic energy of a moving ball can be converted to heat by friction, or it can be converted to potential energy if the ball rolls up a hill. For example, if we say that an energy conversion device is 75% efficient, we mean that 75% of the energy is converted from the first form to the second while the remaining energy either remains in the first form or is converted to other undesired forms of energy.
11.4: Mass Spring Example
https://eng.libretexts.org/Bookshelves/Electrical_Engineering/Electro-Optics/Direct_Energy_(Mitofsky)/11%3A_Calculus_of_Variations/11.04%3A_Mass_Spring_Example
The total energy is given by the Hamiltonian of Equation $\ref{11.4.5}$ . In this example, both the Hamiltonian and the Lagrangian do not explicitly depend on time, $\frac{\partial H}{\partial t} =0$ a...The total energy is given by the Hamiltonian of Equation $\ref{11.4.5}$ . In this example, both the Hamiltonian and the Lagrangian do not explicitly depend on time, $\frac{\partial H}{\partial t} =0$ and $\frac{\partial \mathcal{L}}{\partial t} = 0$ . Following Equation 11.1.6, the ratio of the generalized path to generalized potential is the generalized capacity, and in this example, it is the inverse of the spring constant.
4.4: Antenna Characteristics
https://eng.libretexts.org/Bookshelves/Electrical_Engineering/Electro-Optics/Direct_Energy_(Mitofsky)/04%3A_Antennas/4.04%3A_Antenna_Characteristics
The figure in the upper left is the azimuth plot, the figure in the upper right is the elevation plot, the figure in the lower left is a 3D radiation pattern plot, and the figure in the lower right is...The figure in the upper left is the azimuth plot, the figure in the upper right is the elevation plot, the figure in the lower left is a 3D radiation pattern plot, and the figure in the lower right is the antenna layout.
9.3: Charge Flow in Batteries and Fuel Cells
https://eng.libretexts.org/Bookshelves/Electrical_Engineering/Electro-Optics/Direct_Energy_(Mitofsky)/09%3A_Batteries_and_Fuel_Cells/9.03%3A_Charge_Flow_in_Batteries_and_Fuel_Cells
As above, the direction of the current is the opposite of the direction of the flow of electrons. Reactions occurring are the opposite of the reactions given by Equations $\ref{9.3.1}$ and $\ref{9.3.2}$ . ...As above, the direction of the current is the opposite of the direction of the flow of electrons. Reactions occurring are the opposite of the reactions given by Equations $\ref{9.3.1}$ and $\ref{9.3.2}$ . By definition, the cathode is the electrode which electrons flow towards, and the anode is the electrode which electrons flow away from. These negative ions flow from the cathode to the anode, and positive ions flow from the anode to the cathode.

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