RadSqWl_PhaseShift

RadSqWl_PhaseShift - Main Page 1 Phase Shifting by a...

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Unformatted text preview: Main Page 1 Phase Shifting by a Spherical Square Well The wavefunction is normalized to unit amplitude outside the barrier. For bound states, such as the one at W = 5, D = 5, E = - 0.794, the normalization can be overridden by typing 1 in cell I 13, sheet 2. (But then you'll need to download a fresh copy to reinstate the original normalization.) Vary D, E, L and watch the phase shift. Energy of particle: E= 1.466200 12331 Max Well Depth: D_Max= 10 1150 Depth of Well: D = 1.5 Width of Well: W= 5 1 Adjust Depth of Well with this Slidebar: Angular Momentum: L= Begin to integrate from x = Initial wavefunction value f(0): 1 Numerical step size dx: 0.015 Adjusting the Energy Range: Minimum Energy: E_init=-1 Increment: delta_E= 0.0002 Maximum Energy(automatic): 5.5534 The purpose of this spreadsheet is to illustrate phase shifts in scattering states . Red is the potential. Green is the V = 0 wavefunction. Blue is the wavefunction. Adjust Energy with Slidebar : Don't type in the Cell above! 1 2 3 4 5 6 7 8 9 10-5-4-3-2-1 1 2 3 4 5 Radial Square Well Wavefunction Potential Wavefunction Effective Potl V=0 Wavefn 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. P re no rm a liz e d N o rm a liz e d N o rm a liz e d Position StepPotential Wavefunction 2nd_derivderiv at 1/2Ef ective Pot Max f Wavefunction V = 0 Wavefn 2nd_deriv deriv at 1/2 Max V= V = 0 W a v e fn v(x) 0.62459 0.825 3-1.5-0 1-1.5-0 1 0.015-1.5 0.015-0.04 493 0.9 93 3-1.5 0.0240157874 0.015-0.0219 3 0.9 967 0 .0 18 170 18 2 0.03-1.5 0.029 89 9-0.08 96 0.9 79 8-1.5 0.048015 468 0.029 9505 -0.0439787 0.9 901 0 .0 36 3 4 370 2 0.045-1.5 0.04 959 63 -0.13 36 0.9 59 8-1.5 0.0719832609 0.04 98021-0.06595 0.9 8021 0 .0 5 4 8 6 5 717 0.06-1.5 0.05989 93-0.17 68 0.9 3 3-1.5 0.09590293 7 0.059 5053 -0.08789 5 0.9 6703 0 .0 726 20 79 8 3 0.075-1.5 0.07479 92-0.2 187 0.9 0 05-1.5 0.1 97586014 0.07490107 -0.109819 0.9 505 0 .0 9 0 7310 6 7 0.09-1.5 0.089649 9 -0.26592 0.986016-1.5 0.1435343428 0.0898269 -0.1317042 0.9 308 0 .10 8 1 4 0 5 4 0.105-1.5 0.104 4023-0.30979 0.981369-1.5 0.1672142901 0.10472309 -0.153545 0.9 07 7 0 .126 8 5 8 4 6 7 0.12-1.5 0.1 916076 -0.35345 0.976067-1.5 0.19078263940....
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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_PhaseShift - Main Page 1 Phase Shifting by a...

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