RadSqBarr_Resn (1)

RadSqBarr_Resn (1) - Main Page 1 A Resonance inside a...

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Unformatted text preview: Main Page 1 A Resonance inside a Radial Square Barrier Click the "Using this Spreadsheet" Tab at the bottom for some ideas on exploring wave functions. Energy of particle: E= 1.617100 17171 Depth of Well: D = Width of Well: W= 4 1500 Max Barrier Height: H_Max= 10 Height of Barrier: H= 5 Adjust Height of Barrier with This Slidebar: Breadth of Barrier: B= 1 Angular Momentum: L= Optional Wavefn Scaledown Factor: 1 1 Numerical step size dx: 0.02 Adjusting the Energy Range: Minimum Energy: E_init=-0.1 Increment: delta_E= 0.0001 Maximum Energy(automatic): 3.1767 Use the slider (or click and hold on its ends) to see how the phase changes by on going through the resonance! Adjust Energy with Slidebar : Don't type in the Cell above! 2 4 6 8 10 12 14-5-4-3-2-1 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Radial Square Barrier Wavefunction Potential Wavefunction T a b le Pa ge 2 N U M E R IC A L SO L U T IO N O F SC H R O D IN G E R 'S E Q U A T IO N T he w a v e func tio n a nd its s e c o nd d e riv a tiv e a re fo und a t inte rv a ls n*d e lta _x , w he re n is a n inte g e r, a nd the firs t d e riv a tiv e is fo und a t the "le a p fro g " p o ints , (n + 0 .5 ) *d e lta _x . S o the num e ric a l s te p find ing the c ha ng e in the w a v e func tio n o v e r a n inte rv a l d e lta _x a s um e s it is d e lta _x m ultip lie d b y the v a lue o f the d e riv a tiv e a t the m id p o int o f the inte rv a l. T his is m uc h m o re a c ura te tha n us ing the v a lue o f the d e riv a tiv e a t the b e g in ing o f the inte rv a l. S im ila rly , to find the c ha ng e in the d e riv a tiv e o v e r a n inte rv a l the m e tho d us e d the v a lue o f the s e c o nd d e riv a tiv e in the m id le o f tha t inte rv a l. Position StepPotential Wavefunction 2nd_derivderiv at 1/2 Potential Max f/Sca Wavefunction v(x) 0.14083-0 1 0.02 0.02-0.032342 0.9 9353 0.14201473 1 0.04 0.039 8706 -0.0646 0.9 806 0.2839376054 0.06 0.059 4826 -0.09694 0.9 6121 0.425676815 0.08 0.07987068-0.12916 0.9 3538 0.5671406808 0.1 0.09 7414-0.16129 0.9 0312 0.7082376969 0.12 0.1 954768 -0.193 2 0.9864 6 0.848 765964 0.14 0.13927659 -0.2 52 0.981941 0.98 96 4087 0.16 0.15891542 -0.25698 0.976801 1.1284165179 0.18 0 0.17845145-0.28 57 0.97103 1.26713672 1 0.2 0.19787205-0.319 8 0.96463 1.4050372917 0.2 0.2171646-0.351 8 0.957607 1.5420290269 0.24 0.23631679 -0.38215 0.949 64 1.678023 16 0.26 0.25 31607 -0.41287 0.941707 1.8129321926 0.28 0.2741502 -0.4 3 3 0.93284 1.946 683921 0.3 0.292807-0.4735 0.923 7 2.0791454086 0.32 0.31 274-0.503 6 0.913 03 2.21027 5 07 0.34 0 0.32954046-0.5329 0.902645 2.3 9 79 969 0.36 0 0.347593 5-0.56209 0.891403 2.468168 504 0.38 0 0.365421409 -0.59092 0.879584 2.594761 935 0.4 0.3830131 -0.61937 0.867197 2.7196751414 0.42 0 0.40 35704 -0.64742 0.854249 2.8428298946 0.4 0.4174 201 -0.67505 0.840748 2.9641457916 0.46 0 0.43425697 -0.702 4 0.826703 3.08354 3607 0.48 0 0.450791027-0.72897 0.812124 3.20 9483698 0.5 0.46703 5 -0.75 24 0.797019 3.31628187 6 0.52 0.482973870....
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This note was uploaded on 12/07/2011 for the course PHYSICS 751 taught by Professor Michaelfowler during the Fall '07 term at UVA.

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RadSqBarr_Resn (1) - Main Page 1 A Resonance inside a...

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