RadSqWl_ang_mom_res

RadSqWl_ang_mom_res - Main Page 1 An L = 3 Resonance in a...

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Unformatted text preview: Main Page 1 An L = 3 Resonance in a Radial Square Well which amounts to a well between two radii with barriers on both sides. Energy of particle: E=-0.072440 7878 Depth of Well: D = 13.2 Width of Well: W= 5 1 Wavefunction Scale-Down Factor: 1 (Change this factor to get a better view!) Angular Momentum: L= 3 x_init= Initial wavefunction value f(0): 1 Numerical step size dx: 0.025 Adjusting the Energy Range: Minimum Energy: E_init=-0.23 Increment: delta_E= 0.00002 Maximum Energy(automatic): 0.42534 5873296 The square well (red line) plus the L = 3 angular momentum barrier combine to give an effective potential (green line) See Sheet 3 for how to use this spreadsheet: we start with a bound state , then change it into a resonance . Adjust Energy with Slidebar : Don't type in the Cell above! Click and hold ends for fine adjustment. 2 4 6 8 10 12 14 16-15-10-5 5 10 15 L = 3 Resonance in Radial Square Well Potential Wavefunction Effective Potl 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 1/2Ef ective Pot(Max f)*S Wavefunction v(x) 6E+0 6-13.2-0 1-13.2 0.025-13.2 0.025 479.6718 12.9 18 19186.8 4.2565 4057E-0 9 0.05-13.2 0.3497948 1674.423 54.85238 4786.8 5.95 683294E-0 8 0.075-13.2 1.721 04 4 3649.096 146.0798 2120.13 3 0.0 0 0 293 0.1-13.2 5.37309872 637 .183 305.5093 1 86.8 9.148354070E-0 7 0.125-13.2 13.0108323 9821.519 5 1.0473 754.8 2.21525243 E-0 6 0.15-13.2 26.787015 13934.76 89 .4163 520.13 3 4.560815090E-0 6 0.175-13.2 49.27242 6 18659.92 1365.914 378.63673 8.3892 9210E-0 6 0.2-13.2 83.4202793 23931 1964.189 286.8 1.4203 1712E-0 5 0.2 5-13.2 132.5249 8 29673.6 2706.029 2 3.83704 0.0 0 2 564 0.25-13.2 20 .175718 35805.92 3601.17 178.8 3.408235063E-0 5 0.275-13.2 290.205138 42 39.39 4657.162 145.47 69 0.0 0 4941 0.3-13.2 406.63418 48 79.78 5879.156 120.13 3 6.9234 1468E-0 5 0.325-13.2 5 3.613081 5 628.1 7269.859 10 .40947 9.425936024E-0 5 0.35-13.2 735.35954 62381.74 8 29.402 84.759184 0.0 01252039 0.375-13.2 956.094597 69035.5 105 5.29 72.13 3 3 0.0 01627867 0.4-13.2 1219.97687 75482.95 124 2.36 61.8 0.0 0207 159 0.425-13.2 1531.03598 81617.12 14 82.79 53.235986 0.0 026067 5 0.450....
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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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RadSqWl_ang_mom_res - Main Page 1 An L = 3 Resonance in a...

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