# Energy-dependent potentials and the problem of the equivalent local potential

Abstract : The properties of the wave equation are studied in the case of energy-dependent potentials for bound sates. The nonlinearity induced by the energy dependence requires modification of the standard rules of quantum mechanics. These modifications are briefly recalled. Analytical and numerical solutions are given in the three-dimensional space for power-law radial shape potentials with a linear energy dependence. This last is chosen since it allows the construction of a coherent theory. Among the results, we stress the saturation of the spectrum observed for confining potentials: as the quantum numbers increase, the eigenvalues reach an upper limit. Finally, the problem of the equivalent local potential is discussed. The existence of analytical solutions presents a good opportunity to tackle this problem in detail.
Keywords :
docType_s :
Journal articles
Journal of Physics A Mathematical and Theoretical, 2010, 43, pp.125301. <10.1088/1751-8113/43/12/125301>
Domain :

http://hal.in2p3.fr/in2p3-00464576
Contributor : Sophie Heurteau <>
Submitted on : Wednesday, March 17, 2010 - 2:00:56 PM
Last modification on : Wednesday, March 17, 2010 - 3:00:43 PM

### Citation

R. Yekken, R. J. Lombard. Energy-dependent potentials and the problem of the equivalent local potential. Journal of Physics A Mathematical and Theoretical, 2010, 43, pp.125301. <10.1088/1751-8113/43/12/125301>. <in2p3-00464576>
{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9773445725440979, "perplexity": 1727.8057656435437}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-49/segments/1416931010166.36/warc/CC-MAIN-20141125155650-00236-ip-10-235-23-156.ec2.internal.warc.gz"}