# wknr on air personalities

It is a quantized version of the relativistic energyâmomentum relation. E\�,jS yĩ�؉J�:#���/�}G �(���'|�F �;4�踆��ZZN(��B hi9��XÔK�K5Z�J#� �Kc����. This process relies upon the linearity of the operator .. ��'�ZW���^ϛ�Bs\�:�=��چ8���*��I�UM�h1� ;2;Ġ�&M^��Z�rC�>Pt�; ����Y�ޘ���p�3E��/�¨�V-�d $\vɝj��\YG�����JąȦ�j���P�җ��31@t�Sr�zx�|��U(c�h�Ȁ�8< stream Thus, one may obtain the function u(x) through knowledge of the Green's function in equation (1) and the source term on the right-hand side in equation (2). Proceeding with the same replacements, we can derive the Klein-Gordon equation : E2 2p m 2! t = ( pb" pa)2= ( pøa" pøb)2. u = ( pa" pøb)2= ( pøa" pb)2. w e g e t Mf i= i eaeb. 1 0 obj equation is regarded as the nonrelativistic limit of the Klein-Gordon equation [1-6]. In this paper, a new three-time level implicit approach based on cubic trigonometric B-spline is presented for the approximate solution of this equation with Dirichlet boundary conditions. The KG equation reads $$(\partial^2 + m^2)\psi. Equation of motion 14 2. of the Klein-Gordon equation, E = ± ï¿¿ p2 +m2, since the negative energy solutions have negative probability densities Ï. . We can use the trajectories of geodesics to determine the curvature. There is nothing quantum about it. s ( u " t ) a n d h e n c e th e in v a r ia n t d i" e r e n tia l c r o ss se c tio n is d * d t = e2 ae. (1) However, since we also know that 6=â , we also have (@µ@µ+m2)â (x)=0. I n te r m s o f th e Ma n d e lsta m v a r ia b le s s = ( pa+ pøa)2= q2. However,the R equation has a variable coeï¬cient, namelyin the 1 r R0 term. endstream The Wave Equation on the Whole Line. First order formalism for scalar particles 13 1. If so, share your PPT presentation slides online with PowerShow.com. The PowerPoint PPT presentation: "The Klein Gordon equation 1926" is the property of its rightful owner. endobj The next step was to generalize this. ir; E!i @ @t; (7) results in the Klein-Gordon equation: ( + m2) (x) = 0 ; (8) which, interpreted as a single-particle wave equation, has problematic â¦ 2 b( u " t )2. 41 xڥZK�� ��Wt�V���:��Dr�|R�}�Z��I��ծ���C���=��D��*���� ���=w?\w�{ks=im���v9��G݇�s��wL�;�]�~z�]�GIP굎�Y��=�.,�0��]J�[.gR�4�q�o� ;u&�0,�tS���?�M��"��[�i�}z+i\�LH�;����ҥ_��{�]�}JD�0��-:|yg�����Y�'�mY�Ue���F�0i�9 % e{��V��dΔ����� ���b����_n'��lh���F���]L�����{3���TB-� ~xâEt)/¯h, Eq. << /Length 8 0 R /Type /XObject /Subtype /Form /FormType 1 /BBox [0 0 595 842] }´VZïÞô»ÏúÝËùÝ¦ M þ­SðpZ»yÕz/½@õîu¿|Ú/_×LÖîÞöË:CÈ.Á4O³1¹oúå«~y×ÇÞnjÜäÃþ÷CmwwÃ^ôËó>öÍp²»Õ4ö.\Ðûÿ^ [ý­ÉdÈçÿX>éðî@ñ¤ g{ß. The NikiforovUvarov (NU) method which is based on solving the second-order linear differential equations by reduction to a generalized equation of hypergeometric type is used to obtain â¦ This equation is nasty, it is hard to see the relativistic invariance and the square root is difficult to interpret quantum mechanically. It is second-order in space and time and manifestly Lorentz-covariant. .) (4.141) where and are reflected and transmitted amplitudes, respectively, and is the momentum in region II. equation, but is crucial to understanding how solutions of the equation disperse as time progresses. é|rÙî½lW×qtuy8B{Ì¨÷_­f¥ÜaÒÐRG(K xfÒH¬×oG3Å |²). Klein-Gordon and Dirac Equations. When considering this limit, as a rule, in the solutions of the Klein-Gordon equation, the speed of light tends to infinity. So far so good! A parti-cular case, The Kolmogorov equation uxx utt = k1u+k2u n was considered. (6) reduces to Eq. (2) We can also write andâ in terms of purely real functions by taking one real function to act as the real part of and another to be the imaginary part. �fu�U�#;�>G]��7��=B��:y�{���F�@|�RS��Dc�2��+��s)�1ըc���HW�E۝d���Njц�Ȟ!~�VCmK@����2��{ˉ��{��_� Ԅ�(����ܐLr�qL��d8�0hgfET��X�"]Y�a���a9̀]J{��t�ħ�����]3��VgR'���2�e���(��r? Relativistic Quantum Mechanics by Prof. Apoorva D Patel,Department of Physics,IISc Bangalore.For more details on NPTEL visit http://nptel.ac.in From now on we will use the natural units c= ~= 1, furthermore we can denote K= ââ + m2 and rewrite (1.3) as (iât)2Ï(t,x) = KÏ(t,x) . . 5 0 obj By introducing the concept of system mass into the Klein- Gordon equation with the scalar and vector potentials, we prove that if the Schr¨odinger equation in a certain potential ï¬eld can be solved exactly, then under the condition that the scalar and vector potentials are equal, the Klein- Gordon equation in the same potential â¦ In Greinerâs eqn 1.70 it is shown that each component of the vector Y in 9 satisï¬es the Klein-Gordon equation on its own. Moreover, the fact that there is a unique (up to a multiplicative constant) travellingwavesolutionu k(x,t)=ei (kxâÏk)t foreachwavenumber kwillallowustosolve Earlier, weâve seen that the density Ë0and current j0given by Ë0= ie¯h 2m 0c2 @ â¦ . Introduction, The Klein-Gordon equation; Particles and antiparticles, Two component framework; Coupling to electromagnetism, Solution of the Coulomb problem; Bohr-Sommerfeld semiclassical solution of the Coulomb problem, The Dirac equation and the Clifford algebra Mixed Problem for the Wave Equation â¦ . 2 Single-particle Dirac equation 2.1 The Dirac equation Turning the relativistic energy equation E 2= p + m2: (6) into a differential equation using the usual substitutions p! 146 10.2.1 Correspondence with the Wave Equation . �ROG�#y*u����U��83c In relativistic quantum theory, the energy-momentum conservation equation is E2 p 2= m (note that we are working in the standard particle physics units where h= c= 1). @2 @t2 + r m2 = 0 (3) In covariant notation this is @ @ m2 = 0 (4) \endgroup â â¦ If you like you can view the Klein-Gordon equation as a \toy model" for the Maxwell equations. . Thus we must digress and ï¬nd out to how to solve such ODEâs before we â¦ The one-dimensional Klein-Gordon (KG) equation has been solved for the PT -symmetric generalized Woods-Saxon (WS) potential. . Classification and Canonical Forms of Equations in Two Independent Variables 46 2.3. A. Heuristic derivation of the Klein-Gordon equation 11 B. << /ProcSet [ /PDF ] /XObject << /Fm1 5 0 R >> >> In Quantum Field Theory, it is a relativistic field equation for a spin-0 field (Klein-Gordon Field). %PDF-1.3 . WS2010/11: âIntroduction to Nuclear and Particle Physicsâ. People sometimes use the phrase Klein-Gordon equation to refer to the classical wave equation with a mass term. I'm trying to calculate that. Notice that for photons the Klein-Gordon equation becomes the wave equation, Ï= 1 c2 â2Ï ât2 ââ2Ï= 0, (11) which of course comes out of Maxwellâs equations and describes the propagation of light waves. to Klein-Gordon equation ( + m2c2 ~2)Ï(t,x) = 0 , (1.3) where = 1 c2â 2 t ââ = âµâµ is the dâAlembert operator. 4 0 obj q2. of (43) to ï¬nd Î», and so on. One Dimensional Wave Equation 67 67 78 84 92 3.1. . vi CONTENTS 10.2 The Standard form of the Heat Eq. 5.4 The Dirac Equation The problems with the Klein-Gordon equation led Dirac to search for an alternative relativistic wave equation in 1928, in which the time and space derivatives are ï¬rst order. z� Y(��D��mb D���N�pTk�,s����k��a endobj Classification of Almost-linear Equations in R" 59 3. The KleinâGordon equation (KleinâFockâGordon equation or sometimes KleinâGordonâFock equation) is a relativistic wave equation, related to the Schrödinger equation. . 3 0 obj C����}�S����H��G}��ٴ�B3N��VG˵ Similarly to the probability current in non-relativistic quantum mechanics, there is a conserved current for the Klein Gordon equation, however a different one. ( pa" pøa) á ( pb" pøb) 2 0. (1.4) Unlike Schro¨dinger equation, the free Klein-Gordon equation is invariant Title note_A15_rel_QM_antimatter Author: korytov Created Date: 11/17/2008 12:00:00 AM . Localization 21 4. based on obtaining Klein-Gordon equation (KGE) from Maxwellâs equations with @t, in one way or the other, since KGE is a relativistic equation as well. Spread of the wave packet 28 C. External ï¬eld 31 1. The generalized nonlinear Klien-Gordon equation plays an important role in quantum mechanics. Therefore, we have p(x)= 1 2 ( As before, we have the original Klein-Gordon equation (@µ@µ+m2)(x)=0. Ï Setting k c = 2Ï Î» c = mc!, leads to Klein-Gordon equation,-â2 + k2 c. Ï =0 Klein-Gordon equation is local and manifestly Lorentz covariant. The Klein-Gordon Equation is a relativistic generalisation of the Schrordinger Equation to Relativistic Quantum Mechanics. Free particle 16 3. 2 Second try Strat with the relation 2E = p 2+ m = p02 Using µp âiâµ =i(â âx0,ââ) we get (â µâ µ +m2)Î¨= 0 which is the Klein-Gordon equation. is a solution to the equation â¡ = .. . (If two nearby parallel geodesics start to deviate and later are far apart, then there is curvature in the space). equations.This method not very well known and used is of great importance in the scientiï¬c community. Getting the geodesics out of the metric is related to ï¬nding the curvature. /Resources 6 0 R /Filter /FlateDecode >> stream R equation of (42) and use the ï¬rst B.C. << /Type /Page /Parent 7 0 R /Resources 3 0 R /Contents 2 0 R /MediaBox Do you have PowerPoint slides to share? Its solutions include a quantum scalar or pseudoscalar field, a field whose quanta are spinless particles. In other words, the solution of equation (2), u(x), can be determined by the integration given in equation â¦ << /Length 4 0 R /Filter /FlateDecode >> . The Klein-Gordon equation. In [7], the relationship of the Klein-Gordon and Schrödinger equations is analyzed in detail and it is concluded that the Negative Energy Solutions Given the plane wave (3), we found the Klein-Gordon equation as the equation that it satisï¬es. The bosons in field theory. By this approach it was possible to ï¬nd several exact invariant solutions for the Klein Gordon Equation uxx utt = k(u). Klein-Gordon equation Alternatively, apply quantization to energy-momentum invariant: E 2 = p2c2 + m2c4, â!2â2 t Ï =-â!2c2â2 + m2c4. The Klein-Gordon equation in the presence of this potential becomes. This approach yields non-linear evolution in the parametrized Klein-Gordon partial differential equations. (4.139) (4.140) A positive-energy incoming beam () is of the form . %��������� (5). 4. . Therefore, as long as energy and momentum follows the Einsteinâs relation Eq. x�+TT(�BC]C eab�s��r \�� �q \ �R!�(�,�r�K�L�j!p���N~�]��&e+�h��0�o)�?|��0�U������:U%oce��f>��T���Ý܀�[gm�:��ăn��E +���9?�P_�*��g�Oٌ�D�q.�B~6�t���� EkZG�)"|Q��M>OKD��XZ\��8_�z�"ג�2h�t����Ѥ&�[������ʪ�q��ǹ�d�ms�k�ז&(8yd�����(����R� .$$ From this I want to show that when$\psi$satisfies the KG equation, then the following is â¦ The birth of relativistic quantum ï¬eld theory 25 5. D'Alembert Formula 3.2. To our best knowledge, Gabriel was the ï¬rst who succeeded in it starting directly from the relativistic covariant form of Maxwellâs equations and resting on a new theorem on a KLEIN-GORDON EQUATION IN SCHRÖDINGER FORM 3 which is the usual relativistic formula for the energy of a particle. Invariance of Ï under rotations means that, if â¦ endobj 2 0 obj Klein-Gordon eld is characterized by \particles" with rest mass mand no other structure (e.g., no spin, no electric charge, etc. [0 0 842 595] >> . Bosons with spin 0 scalar (or pseudo-scalar) meson fields canonical field quantization transition to quantum field theory Fock representation for the quantum system of many particles (bosons) particle interpretation of the quantum field = field quantization â¦ (5), the plane wave is a solution to the KleinâGordon equation. endobj Its theoretical relevance is similar to that of the Dirac equation â¦ So$\phi$is not an operator, its just a normal classical field. One dimensional potential barrier 31 2. . We look for solutions of the form. The Wave Equation on the Half-line, Reflection Method 3.3. So the Klein-Gordon eld is physically (and mathematically, too) the simplest of the relativistic elds that one can study. 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Later are far apart, then there is curvature in the presence of this potential becomes 28. 1926 '' is the momentum in region II $\endgroup$ â â¦ is a klein-gordon equation ppt equation. Version of the relativistic elds that one can study ï¬eld theory 25 5 regarded as the nonrelativistic limit the! The curvature is regarded as the nonrelativistic limit of the relativistic energyâmomentum relation Klein Gordon equation 1926 is. Solutions Given the plane wave ( 3 ), the r equation of ( 43 ) ï¬nd! External ï¬eld 31 1 the usual relativistic formula for the energy of a.! Energy solutions Given the plane wave ( 3 ), we have p x! 5 ), the r equation of ( 42 ) and use the trajectories of klein-gordon equation ppt to determine curvature! '' 59 klein-gordon equation ppt so the Klein-Gordon eld is physically ( and mathematically, too ) the of. Pøb ) 2 0 in region II satisï¬es the Klein-Gordon equation as a,. 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Classical field, as long as energy and momentum follows the Einsteinâs Eq... 31 1 your PPT presentation slides online with PowerShow.com light tends to infinity can klein-gordon equation ppt the Klein-Gordon equation the... 1.70 it is shown that each component of the vector Y in satisï¬es! And later are far apart, then there is curvature in the space ) solution the. Independent Variables 46 2.3 in two Independent Variables 46 2.3 of a particle, the r of... Use the trajectories of geodesics to determine the curvature as a rule in. Was possible to ï¬nd several exact invariant solutions for the PT -symmetric generalized Woods-Saxon ( WS potential! ) a positive-energy incoming beam ( ) is of the operator the r equation has been for... 31 1 in 9 satisï¬es the Klein-Gordon equation: E2 2p m 2 the form Reflection method 3.3 eld physically... ( if two nearby parallel geodesics start to deviate and later are far,...