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RadSqWl_ang_mom_res

# RadSqWl_ang_mom_res - Main An L = 3 Resonance in a Radial...

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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 0 Wavefunction Scale-Down Factor: 1 (Change this factor to get a better view!) Angular Momentum: L= 3 x_init= 0 Initial wavefunction value f(0): 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. 0 2 4 6 8 10 12 14 16 -15 -10 -5 0 5 10 15 L = 3 Resonance in Radial Square Well Potential Wavefunction Effective Potl

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Table Page 2 NUMERICAL SOLUT ION OF SCHRODINGER'S EQUAT ION The wavefunction and its second derivative are found at intervals n*delta_x, where n is an integer, and the first derivative is found at the "leapfrog" points, (n + 0.5)*delta_x. So the numerical step finding the change in the wavefunction over an interval delta_x assumes it is delta_x multiplied by the value of the derivative at the midpoint of the interval. This is much more accurate than using the value of the derivative at the beginning of the interval. Similarly, to find the change in the derivative over an interval the method used the value of the second derivative in the middle of that interval. Position StepPotential Wavefunction 2nd_deriv deriv at 1/2Effective Potl(Max f)*S Wavefunction v(x) 6E+006 0 -13.2 0 -0 1 -13.2 0 0.025 -13.2 0.025 479.6718 12.9918 19186.8 4.256554057E-009 0.05 -13.2 0.34979488 1674.423 54.85238 4786.8 5.955683294E-008 0.075 -13.2 1.72110444 3649.096 146.0798 2120.1333 0.000000293 0.1 -13.2 5.37309872 6377.183 305.5093 1186.8 9.148354070E-007 0.125 -13.2 13.0108323 9821.519 551.0473 754.8 2.215252433E-006 0.15 -13.2 26.787015 13934.76 899.4163 520.13333 4.560815090E-006 0.175 -13.2 49.2724226 18659.92 1365.914 378.63673 8.389229210E-006 0.2 -13.2 83.4202793 23931 1964.189 286.8 1.420331712E-005 0.225 -13.2 132.524998 29673.6 2706.029 223.83704 0.000022564 0.25 -13.2 200.175718 35805.92 3601.177 178.8 3.408235063E-005 0.275 -13.2 290.205138 42239.39 4657.162 145.47769 0.000049411 0.3 -13.2 406.63418 48879.78 5879.156 120.13333 6.923441468E-005 0.325 -13.2 553.613081 55628.1 7269.859 100.40947 9.425936024E-005 0.35 -13.2 735.359544 62381.74 8829.402 84.759184 0.0001252039 0.375 -13.2 956.094597 69035.55 10555.29 72.133333 0.0001627867 0.4 -13.2 1219.97687 75482.95 12442.36 61.8 0.0002077159 0.425 -13.2 1531.03598 81617.12 14482.79 53.235986 0.0002606775 0.45 -13.2 1893.10579 87332.19 16666.1 46.059259 0.0003223243 0.475 -13.2 2309.75822 92524.38 18979.21 39.985596 0.0003932644 0.5 -13.2 2784.23839 97093.19 21406.54 34.8 0.0004740504 0.525 -13.2 3319.40179 100943 23930.1 30.337415 0.0005651685 0.55 -13.2 3917.65428 103982 26529.65 26.469421 0.0006670283 0.575 -13.2 4580.89541 106127 29182.82 23.094896 0.0007799532 0.6 -13.2 5310.46601 107302 31865.38 20.133333 0.0009041714 0.625 -13.2 6107.1004 107439 34551.35 17.52 0.0010398081 0.65 -13.2 6970.88404 106479 37213.32 15.202367 0.0011868778 0.675 -13.2 7901.217 104374 39822.67 13.137449 0.0013452783 0.7 -13.2 8896.78383 101087 42349.86 11.289796 0.0015147857 0.725 -13.2 9955.53026 96592.58 44764.67 9.6299643 0.0016950501 0.75 -13.2 11074.647 90876 47036.57 8.1333333 0.0018855934 0.775 -13.2 12250.5614 83936.29 49134.98 6.7791883 0.0020858071 0.8 -13.2 13478.9359 75784.51 51029.59 5.55 0.0022949528 0.825 -13.2 14754.6757 66444.64 52690.71 4.430854 0.002512163 0.85 -13.2 16071.9434 55953.45 54089.55 3.4089965 0.0027364438 0.875 -13.2 17424.182 44360.39 55198.55 2.4734694 0.0029666789 0.9 -13.2 18804.1459 31727.39 55991.74 1.6148148 0.0032016345 0.925 -13.2 20203.9394 18128.5 56444.95 0.8248356 0.0034399664 0.95 -13.2 21615.0632 3649.463 56536.19 0.0963989 0.0036802274 0.975 -13.2 23028.4679 -11612.9 56245.87 -0.576726 0.0039208767 1 -13.2 24434.6145 -27551.5 55557.08 -1.2 0.0041602903 1.025 -13.2 25823.5415 -44049.5 54455.84 -1.778227 0.004396772 1.05 -13.2 27184.9375 -60981.4 52931.31 -2.315646 0.0046285662 1.075 -13.2 28508.2202 -78214.3 50975.95 -2.816009 0.0048538712 1.1 -13.2 29782.6189 -95608.3 48585.74 -3.282645 0.0050708531 1.125 -13.2 30997.2625 -113018 45760.28 -3.718519 0.0052776609 1.15 -13.2 32141.2695 -130295 42502.89 -4.126276 0.005472442 1.175 -13.2 33203.8418 -147287 38820.72 -4.508284 0.0056533579 1.2 -13.2 34174.3598 -163840 34724.73 -4.866667 0.0058186004 1.225 -13.2 35042.478 -179799 30229.75 -5.203332 0.0059664081 1.25 -13.2 35798.2216 -195013 25354.42 -5.52 0.0060950826 1.275 -13.2 36432.0822 -209331 20121.15 -5.818224 0.0062030051 1.3 -13.2 36935.1111 -222607 14555.98 -6.099408 0.0062886519 1.325 -13.2 37299.0106 -234700 8688.488 -6.364827 0.0063506102 1.35 -13.2 37516.2228 -245476 2551.586 -6.615638 0.0063875932 1.375 -13.2 37580.0125 -254809 -3818.65 -6.852893 0.0063984542 1.4 -13.2 37484.5462 -262583 -10383.2 -7.077551 0.0063821999 1.425 -13.2 37224.9653 -268692 -17100.5 -7.290489 0.0063380031 1.45 -13.2 36797.4522 -273040 -23926.5 -7.492509 0.0062652138 1.475 -13.2 36199.2892 -275545 -30815.2 -7.684344 0.0061633693 1.5 -13.2 35428.9103 -276141 -37718.7 -7.866667 0.0060322029 1.525 -13.2 34485.9433 -274772 -44588 -8.040097 0.0058716513 1.55 -13.2 33371.2438 -271400 -51373 -8.205203 0.0056818601 1.575 -13.2 32086.9189 -266003 -58023.1 -8.362509 0.0054631882 1.6 -13.2 30636.3423 -258573 -64487.4 -8.5125 0.0052162099 1.625 -13.2 29024.1579 -249120 -70715.4 -8.655621 0.0049417159 1.65 -13.2 27256.2737 -237671 -76657.1 -8.792287 0.0046407121 1.675 -13.2 25339.8454 -224269 -82263.8 -8.922878 0.0043144169 1.7 -13.2 23283.2492 -208974 -87488.2 -9.047751 0.0039642564 1.725 -13.2 21096.044 -191864 -92284.8 -9.167234 0.0035918581 1.75 -13.2 18788.9237 -173031 -96610.6 -9.281633 0.0031990428 1.775 -13.2 16373.6591 -152583 -100425 -9.391232 0.0027878146 1.8 -13.2 13863.0303 -130643 -103691 -9.496296 0.0023603495 1.825 -13.2 11270.7495 -107350 -106375 -9.597073 0.0019189822 1.85 -13.2 8611.37508 -82853.1 -108446 -9.693791 0.0014661913 1.875 -13.2 5900.21752 -57316.1 -109879 -9.786667 0.0010045838 1.9 -13.2 3153.23743 -30912.6 -110652 -9.8759 0.000536877 1.925 -13.2 386.936948 -3826.51 -110748 -9.96168 6.588072137E-005 1.95 -13.2 -2381.7551 23750.25 -110154 -10.04418 -0.0004055228 1.975 -13.2 -5135.6033 51618.62 -108863 -10.12357 -0.0008743989 2 -13.2 -7857.1898 79574.16 -106874 -10.2 -0.0013377821 2.025 -13.2 -10529.042 107409 -104189 -10.27362 -0.0017926975 2.05 -13.2 -13133.765 134912 -100816 -10.34456 -0.0022361832 2.075 -13.2 -15654.167 161872 -96769.3 -10.41295 -0.0026653124 2.1 -13.2 -18073.4 188080 -92067.3 -10.47891 -0.0030772161
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RadSqWl_ang_mom_res - Main An L = 3 Resonance in a Radial...

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