Geodesic
Comment on failure of excited-state energy calculation of analytical transfer matrix method for the potential
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 51 (2011) no. 3, pp. 470-479

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The analytical transfer matrix method is applied to the quantum mechanical bound-state problem potential with $V(x)=(1/2)kx^2+\lambda x^4$. It is found that numerical values of phase contribution are unstable when compared with standard methods like numerical shoot method, WKB approximation, this leads to substantial errors in excited-state energy calculation. 
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     author = {A. Hutem},
     title = {Comment on failure of excited-state energy calculation of analytical transfer matrix method for the potential},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {470--479},
     publisher = {mathdoc},
     volume = {51},
     number = {3},
     year = {2011},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2011_51_3_a5/}
}
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A. Hutem. Comment on failure of excited-state energy calculation of analytical transfer matrix method for the potential. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 51 (2011) no. 3, pp. 470-479. http://geodesic.mathdoc.fr/item/ZVMMF_2011_51_3_a5/