...The central working equation for studying laser–atom interactions is the TDSE (1.2) ¹ and, in one form or another, we will eventually face the problem of its approximation by either a direct numerical method or physically motivated assumptions. The latter case may entail considerable...

... Department Stanford University Stanford , n.d. ), CA 94305-4115. Zandieh , M.   et al. , J. Math. Behav.   33 , 209 – 229 ( 2014 ). 10.1016/j.jmathb.2013.11.007 Physics Equations in Physics Education Mathematics equations and physics equations The verbalization of physics equations...

... have shown all the main equations for quantum mechanics and spectroscopy in Chap. 2, but we are not done. They are not easily measurable. They are still in integral or differential form. And we can improve their utility by solving them analytically using calculus and by simplifying the solutions...

... Methods Learning problem-solving production rules Introduction Student difficulties with algebraic and mathematical complexity Selecting equations from an initial, principle-based problem description Worked examples Instructional Problem-Solving Approaches Motivated by the Expert Solution Methods...

.... Res.   13 , 020132 ( 2017 ). 10.1103/PhysRevPhysEducRes.13.020132 Succi , S. , The Lattice Boltzmann Equation for Fluid Dynamics and Beyond ( Oxford University Press , Oxford , 2001 ). Suzuki , M. , “ Fourier-spectral methods for Navier-Stokes equations in 2D ” ( 2014 ), see...

.../the speed of learning (from quick to gradual nature of learning) Learning is quick Learning is a gradual process Table 11.5 Epistemological components to map university physics students’ epistemological mindsets towards the understanding of physics equations (analyzing interviews, Domert et al...

...Table 18.1 Technical-structural distinction concerning the role of mathematics in physics, similar to Karam (2014). Technical (instrumental, procedural) Structural (relational, organizational) Blindly use an equation to solve quantitative problems (plug and chug) Derive...

... differential equations to calculate macroscopic properties such as system temperatures, which are in turn utilized in event-based microscopic kMC simulations to perform the dissolution of individual elements of the wood chips ( Choi and Kwon, 2019a , 2019b ; Son et al., 2020 ; and Lee et al...

... parameters. We express the total energy of a system in terms of a number of order parameter fields. Once the order parameter fields are correctly chosen to adequately describe all the physical interactions in a system, we develop a set of evolution equations (Cahn-Hilliard equation for conserved order...

... with multivariate reasoning The way in which the source moves can affect the propagation velocity of the pulse Relying on equations Waves What does wavelength depend on? Pulses after overlap Other interesting findings Difficulties with superposition of pulses Investigation tools and interventions Sound...

...) large computational requirements due to the dynamic simulation of highly-coupled partial differential equations (PDEs) defined over a time-dependent spatial domain. Typically, the high-fidelity hydraulic fracturing simulators used in these studies require several days, sometimes over weeks, to compute...

... is called sparse identification. Let the following equation represent the governing dynamics of a process system: (10.1) d d t x ( t ) = f ( x ( t ) , u ( t ) ) where x (t) and u (t) are the vectors corresponding to the state of the system and applied...

... in the liquid absorbent, respectively; f_i represents the gas phase fugacity of the gas i in the mixed system; P i S is the saturated vapor pressure of gas i calculated from the Antoine equation. H_i represents the Henry's coefficient of gas...

... 0.31 FCI 13 0.56 0.31 FCI 14 0.36 FCI 15 0.65 FIG. 24.1 Scree plot of the first 15 items on the FCI (black line). The red line presents the parallel analysis for 15 items. FIG. 24.2 Illustration of the effects of nested data. FIG. 24.3 Structural equation models. FIG. 24.4 Scree...

.../PhysRevPhysEducRes.13.020132 Succi , S. , The Lattice Boltzmann Equation for Fluid Dynamics and Beyond ( Oxford University Press , Oxford , 2001 ). Suzuki , M. , “ Fourier-spectral methods for Navier-Stokes equations in 2D ” ( 2014 ), see http://www.math.mcgill.ca/gantumur/math595f14...

... In all the table: SE = Schrödinger equation Table 8.1 Questionnaires on QM for high school/undergraduate: phenomenological contexts; contents; concepts. Notes: MC: Multiple choice; ME: Motivation/explanation; OE: Open-ended question; TF: thrue/false; FPS: five-point scale from 1 ∼ “strongly...

... ). Symmetry is a prolonged beauty of physics that many physicists have considered before. In Greek philosophy, symmetria means balanced, rhythmical and finely detailed human bodies or objects. In physics, symmetry comprises diverse forms of equations or figures. Weyl (1980) and Zee (1999...