{"id":87910,"date":"2015-05-20T03:00:00","date_gmt":"2015-05-20T00:00:00","guid":{"rendered":"http:\/\/www.fyysika.ee\/?guid=ba078aa870da9bbb2bbb3f8eebd40f35"},"modified":"2015-05-20T03:00:00","modified_gmt":"2015-05-20T00:00:00","slug":"new-shape-resonances-in-one-dimension","status":"publish","type":"post","link":"https:\/\/www.fyysika.ee\/?p=87910","title":{"rendered":"New shape resonances in one dimension"},"content":{"rendered":"<p>Hitherto, a finitely thick barrier next to a well or a rigid wall has been considered the potential<br \/>\nof simplest shape giving rise to resonances (metastable states) in one dimension: x\u2208 (\u2212\u221e, \u221e). In<br \/>\nsuch a potential, there are three real turning points at an energy below the barrier. Resonances are<br \/>\nGamow\u2019s (time-wise) decaying states with discrete complex energies ##IMG##<br \/>\n[http:\/\/ej.iop.org\/images\/0143-0807\/36\/4\/048001\/ejp512438ieqn1.gif]<br \/>\n{$({{mathcal{E}}_{n}}={{E}_{n}}-{rm i}{{Gamma }_{n}}\/2)$} . These are also spatially catastrophic<br \/>\nstates that manifest as peaks\/wiggles in Wigner\u2019s reflection time delay at ##IMG##<br \/>\n[http:\/\/ej.iop.org\/images\/0143-0807\/36\/4\/048001\/ejp512438ieqn2.gif] {$E={{epsilon }_{n}}approx<br \/>\n{{E}_{n}}$} . Here we explore potentials with simpler shapes giving rise to resonances\u2014two-piece<br \/>\nrising potentials having just one-turning point. We demonstrate our point by using rising<br \/>\nexponential profile in various ways.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Hitherto, a finitely thick barrier next to a well or a rigid wall has been considered the potential<br \/>\nof simplest shape giving rise to resonances (metastable states) in one dimension: x\u2208 (\u2212\u221e, \u221e). In<br \/>\nsuch a potential, there are three real turnin&#8230;<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_genesis_hide_title":false,"_genesis_hide_breadcrumbs":false,"_genesis_hide_singular_image":false,"_genesis_hide_footer_widgets":false,"_genesis_custom_body_class":"","_genesis_custom_post_class":"","_genesis_layout":"","footnotes":""},"categories":[178],"tags":[],"class_list":{"0":"post-87910","1":"post","2":"type-post","3":"status-publish","4":"format-standard","6":"category-rss-fuusikaharidus","7":"entry"},"_links":{"self":[{"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=\/wp\/v2\/posts\/87910","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=87910"}],"version-history":[{"count":0,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=\/wp\/v2\/posts\/87910\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=87910"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=87910"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=87910"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}