Scrodinger wave equation
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The document derives the time-independent Schrodinger wave equation. It begins by separating the wave function ψ into a spatial component ψ(x,y,z) and temporal component g(t). Substituting this into the general wave equation allows separating variables, resulting in ψ(x,y,z) satisfying -ħ2/2m∇2ψ + Vψ = Eψ, where H is the Hamiltonian operator. This eigenvalue equation describes the energy levels of quantum mechanical systems.
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1) Theorems by Geraghty, Amini-Harandi and Emami, and Gnana Bhaskar and Lakshmikantham establish the existence of unique fixed points for contraction mappings on complete metric spaces and partially ordered metric spaces.
2) Choudhury and Kundu extended these results to Geraghty contractions by introducing an altering distance function.
3) GVR Babu and P. Subhashini further generalized the results to coupled fixed points for Geraghty contractions using an altering distance
Time Delay and Mean Square Stochastic Differential Equations in Impetuous Sta...
This paper specially exhibits about the time delay and mean square stochastic differential equations in impetuous stabilization is analyzed. By projecting a delay differential inequality and using the stochastic analysis technique, a few present stage for mean square exponential stabilization are survived. It is express that an unstable stochastic delay system can be achieved some stability by impetuous. This example is also argued to derived the efficiency of the obtained results. G. Pramila | S. Ramadevi"Time Delay and Mean Square Stochastic Differential Equations in Impetuous Stabilization" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-2 | Issue-3 , April 2018, URL: http://www.ijtsrd.com/papers/ijtsrd11062.pdf http://www.ijtsrd.com/humanities-and-the-arts/other/11062/time-delay-and-mean-square-stochastic-differential-equations-in-impetuous-stabilization/g-pramila
2018 Geometri Transformasi Perkalian 5 Isometri Kelompok 8 Rombel 3
This document summarizes the steps to draw the shadow of a triangle under five isometric transformations. It begins by stating the given information: a triangle ΔUVW and the transformations (S B)(R A,φ1)(G KL)(G PQ. Mt)(MS). It then shows each step of applying the transformations to arrive at the final transformed triangle R M,φ9(ΔUVW). The proof is done indirectly by relating the angles and lines created at each step. Diagrams are provided to illustrate the transformations.
Modeling monthly average daily diffuse radiation for dhaka, bangladesh
Abstract The diffuse part of solar radiation is one of the elements necessary for the design and evaluation of energy production of a solar system. However, in most cases, when radiometric measurements are made, only global radiation is available. To remedy this situation, this paper presents a model of the scattered radiation measured on a horizontal surface for the capital city of Bangladesh. The correlation established for the chosen site was compared to the work of Liu anf Jordan, Page, Collares Pereira and Rabl, Modi and Sukhatme and Gupta el al. Keywords: Diffuse Radiation, Clearness Index, Regression analysis, Horizontal Radiation.
Trajectory clustering using adaptive Euclidean distances
The presentation deals with the clustering of trajectories of moving objects. A k-means-like algorithm based on a Euclidean distance between piece-wise linear curves is used. The main novelty of the paper is the opportunity of considering in the clustering procedure a step that automatically weights the importance of sub-trajectories of the original ones. The algorithm uses an adaptive distances approach and a cluster-wise weighting. The proposed algorithm is tested against some workbench trajectory datasets.
Presented at SIS 2019, Milan.
On The Numerical Solution of Picard Iteration Method for Fractional Integro -...
ff(xx),
ff(xx) + λλ ∫ KK(xx, tt)uu0(tt)dddd,
xx
0
(14)
1. This document discusses the Picard iteration method for solving fractional integro-differential equations. The fractional derivative is considered in the Caputo sense.
2. The proposed Picard iteration method reduces fractional integro-differential equations to standard integral equations of the second kind.
3. Some test problems are considered to demonstrate the accuracy and convergence of the presented Picard iteration method for solving fractional integro-differential equations. Numerical results show the approach is easy and accurate.
Indoor Heading Estimation
Quaternion-Based Unscented Kalman Filter for Accurate Indoor Heading Estimation Using Wearable Multi-Sensor System
Duel of cosmological screening lengths
E. Canay and M. Eingorn
Physics of the Dark Universe 29 (2020) 100565
DOI: 10.1016/j.dark.2020.100565
https://authors.elsevier.com/a/1aydL7t6qq5DB0
https://arxiv.org/abs/2002.00437
Two distinct perturbative approaches have been recently formulated within General Relativity, arguing for the screening of gravity in the ΛCDM Universe. We compare them and show that the offered screening concepts, each characterized by its own interaction range, can peacefully coexist. Accordingly, we advance a united scheme, determining the gravitational potential at all scales, including regions of nonlinear density contrasts, by means of a simple Helmholtz equation with the effective cosmological screening length. In addition, we claim that cosmic structures may not grow at distances above this Yukawa range and confront its current value with dimensions of the largest known objects in the Universe.
Similar to Scrodinger wave equation (20)
Vol13 iss1 68-70_a_note_on_generalization_of_classic
Vol13 iss1 68-70_a_note_on_generalization_of_classic
Physics, Astrophysics & Simulation of Gravitational Wave Source (Lecture 1)
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2018 Geometri Transformasi Perkalian 5 Isometri Kelompok 1 Rombel 3
2018 Geometri Transformasi Perkalian 5 Isometri Kelompok 1 Rombel 3
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2018 Geometri Transformasi Perkalian 5 Isometri Kelompok 7 Rombel 3
2018 Geometri Transformasi Perkalian 5 Isometri Kelompok 7 Rombel 3
SIAM-AG21-Topological Persistence Machine of Phase Transition
SIAM-AG21-Topological Persistence Machine of Phase Transition
Calculating transition amplitudes by variational quantum eigensolvers
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Time Delay and Mean Square Stochastic Differential Equations in Impetuous Sta...
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2018 Geometri Transformasi Perkalian 5 Isometri Kelompok 8 Rombel 3
2018 Geometri Transformasi Perkalian 5 Isometri Kelompok 8 Rombel 3
Modeling monthly average daily diffuse radiation for dhaka, bangladesh
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On The Numerical Solution of Picard Iteration Method for Fractional Integro -...
On The Numerical Solution of Picard Iteration Method for Fractional Integro -...
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Scrodinger wave equation
- 1. Time Independent Schrodinger Wave Equation Dr. Sujit K. Shah, Tribhuvan University, Nepal 7/15/2020 1
- 2. Two basic observations • The wave character of the electron These observations lead us to use a wave equation and attempt to introduce particle character through the de Broglie relation • The probability character of our measurements Dr. Sujit K. Shah, Tribhuvan University, Nepal 7/15/2020 2
- 3. The general partial differential equation of wave motion is: 𝜕2 𝜓 𝜕𝑥2 + 𝜕2 𝜓 𝜕𝑦2 + 𝜕2 𝜓 𝜕𝑧2 = 1 𝑣2 𝜕2 𝜓 𝜕𝑡2 𝛻2 = 𝜕2 𝜕𝑥2 + 𝜕2 𝜕𝑦2 + 𝜕2 𝜕𝑧2 known as Laplacian operator 𝜕2 𝜕𝑥2 + 𝜕2 𝜕𝑦2 + 𝜕2 𝜕𝑧2 𝜓 = 1 𝑣2 𝜕2 𝜓 𝜕𝑡2 𝛻2 𝜓 = 1 𝑣2 𝜕2 𝜓 𝜕𝑡2 1 Dr. Sujit K. Shah, Tribhuvan University, Nepal 7/15/2020 3
- 4. The function 𝜓 can be resolved in two functions; function of space coordinates 𝜓(𝑥,𝑦,𝑧) and function of time 𝑔(𝑡) 𝜓 = 𝜓(𝑥,𝑦,𝑧) 𝑔(𝑡) Substituting this to equation 1 𝛻2 𝜓(𝑥,𝑦,𝑧) 𝑔(𝑡) = 1 𝑣2 𝜕2 𝜓(𝑥,𝑦,𝑧) 𝑔(𝑡) 𝜕𝑡2 𝑔(𝑡) 𝛻2 𝜓(𝑥,𝑦,𝑧) = 1 𝑣2 𝜓(𝑥,𝑦,𝑧) 𝜕2 𝑔(𝑡) 𝜕𝑡2 Dr. Sujit K. Shah, Tribhuvan University, Nepal 7/15/2020 4
- 5. In order to separate time dependence, several wave functions may chosen for 𝑔(𝑡), such as 𝑒(2𝜋𝑖𝜈𝑡) or 𝑆𝑖𝑛 2𝜋𝜈𝑡 If we substitute 𝑔(𝑡) = 𝑒(2𝜋𝑖𝜈𝑡) In order to separate time dependence, several wave functions may chosen for 𝑔(𝑡), such as 𝑒(2𝜋𝑖𝜈𝑡) or 𝑆𝑖𝑛 2𝜋𝜈𝑡 If we substitute 𝑔(𝑡) = 𝑒(2𝜋𝑖𝜈𝑡) 𝑒(2𝜋𝑖𝜈𝑡) 𝛻2 𝜓(𝑥,𝑦,𝑧) = 1 𝑣2 𝜓(𝑥,𝑦,𝑧) 𝜕2 𝑒(2𝜋𝑖𝜈𝑡) 𝜕𝑡2 Dr. Sujit K. Shah, Tribhuvan University, Nepal 7/15/2020 5
- 6. 𝑒(2𝜋𝑖𝜈𝑡) 𝛻2 𝜓(𝑥,𝑦,𝑧) = 1 𝑣2 𝜓 𝑥,𝑦,𝑧 (−4𝜋2 𝜈2 )𝑒(2𝜋𝑖𝜈𝑡) 𝜕𝑒(𝟐𝝅𝒊𝝂𝑡) 𝜕𝑡 = (𝟐𝝅𝒊𝝂)𝑒(𝟐𝝅𝒊𝝂𝑡) 𝛻2 𝜓(𝑥,𝑦,𝑧) = −4𝜋2 𝜈2 𝑣2 𝜓 𝑥,𝑦,𝑧 It is seen that the variable, 𝑡, cancels, and we have succeeded in separating out the time dependence leaving a wave equation that depends only on space coordinates. 2 Dr. Sujit K. Shah, Tribhuvan University, Nepal 7/15/2020 6
- 7. Equation 2 represents the wave portion. 𝛻2 𝜓(𝑥,𝑦,𝑧) = −4𝜋2 𝜆2 𝜓 𝑥,𝑦,𝑧 𝜈 = 𝑣/𝜆 The particle character is introduced using de Broglie equation: 𝜆 = ℎ 𝑚𝑣 𝛻2 𝜓(𝑥,𝑦,𝑧) = −4𝜋2 𝑚2 𝑣2 ℎ2 𝜓 𝑥,𝑦,𝑧 Dr. Sujit K. Shah, Tribhuvan University, Nepal 7/15/2020 7
- 8. Total energy 𝐸 = 𝐾. 𝐸. + 𝑉 1 2 𝑚𝑣2 = 𝐸 − 𝑉 𝛻2 𝜓(𝑥,𝑦,𝑧) = −8𝜋2 𝑚 ℎ2 (𝐸 − 𝑉)𝜓 𝑥,𝑦,𝑧 Dr. Sujit K. Shah, Tribhuvan University, Nepal 7/15/2020 8
- 9. 𝛻2 𝜓(𝑥,𝑦,𝑧) = −8𝜋2 𝑚 ℎ2 (𝐸 − 𝑉)𝜓 𝑥,𝑦,𝑧 − ℎ2 8𝜋2 𝑚 𝛻2 𝜓(𝑥,𝑦,𝑧) = (𝐸 − 𝑉)𝜓 𝑥,𝑦,𝑧 − ℎ2 8𝜋2 𝑚 𝛻2 𝜓 𝑥,𝑦,𝑧 + 𝑉𝜓 𝑥,𝑦,𝑧 = 𝐸𝜓 𝑥,𝑦,𝑧 (− ℎ2 8𝜋2 𝑚 𝛻2 + 𝑉)𝜓 𝑥,𝑦,𝑧 = 𝐸𝜓 𝑥,𝑦,𝑧 𝐻𝜓 𝑥,𝑦,𝑧 = 𝐸𝜓 𝑥,𝑦,𝑧 Dr. Sujit K. Shah, Tribhuvan University, Nepal 7/15/2020 9
- 10. 𝐻𝜓 𝑥,𝑦,𝑧 = 𝐸𝜓 𝑥,𝑦,𝑧 𝐻 = (− ℎ2 8𝜋2 𝑚 𝛻2 + 𝑉) Hamiltonian Operator An equation, where the operator, operating on a function, produces a constant times the function, is called an eigenvalue equation. The function is called an eigenfunction, and the resulting numerical value is called the eigenvalue. Eigenvalue Eigenfunction Dr. Sujit K. Shah, Tribhuvan University, Nepal 7/15/2020 10