{"id":42175,"date":"2026-03-28T07:34:17","date_gmt":"2026-03-28T07:34:17","guid":{"rendered":"https:\/\/www.tugraz-verlag.at\/gesamtverzeichnis\/unkategorisiert\/empty-product-container-3\/"},"modified":"2026-03-28T11:35:17","modified_gmt":"2026-03-28T09:35:17","slug":"superoscillations-and-their-schroedinger-time-evolution-ebook","status":"publish","type":"product","link":"https:\/\/www.tugraz-verlag.at\/en\/gesamtverzeichnis\/mathematik-physik-und-geodaesie\/superoscillations-and-their-schroedinger-time-evolution-ebook\/","title":{"rendered":"Superoscillations and their Schr\u00f6dinger time evolution"},"content":{"rendered":"<p>Superoscillations are functions with the paradoxical behavior of oscillating (at least<br \/>locally) faster than their largest Fourier component. For example, plane waves with<br \/>small frequencies (e.g. red light) can interfere in such a way that a resulting wave<br \/>with arbitrary large frequency is created (e.g. blue light or theoretically even a gamma<br \/>ray).<br \/>Due to the wave-particle duality in quantum mechanics, also particles can exhibit<br \/>this superoscillatory behavior. One of the main questions in this context then is:<br \/>What happens when a particle with a superoscillating wave function interacts with a<br \/>potential? Does this delicate interference effect persists in time, or is it destroyed by<br \/>the external force?<br \/>The aim of this thesis is to introduce a universally valid and mathematically precise<br \/>formalism of the concept of superoscillationslationen, which in particular covers all<br \/>the existing results of the past literature. Moreover, a method is developed which<br \/>ensures the time persistence of superoscillations for whole classes of potentials.<br \/><\/p>","protected":false},"excerpt":{"rendered":"<p>Superoscillations are functions with the paradoxical behavior of oscillating (at least<br \/>locally) faster than their largest Fourier component. For example, plane waves with<br \/>small frequencies (e.g. red light) can interfere in such a way that a resulting wave<br \/>with arbitrary large frequency is created (e.g. blue light or theoretically even a gamma<br \/>ray).<br \/>Due to the wave-particle duality in quantum mechanics, also particles can exhibit<br \/>this superoscillatory behavior. One of the main questions in this context then is:<br \/>What happens when a particle with a superoscillating wave function interacts with a<br \/>potential? Does this delicate interference effect persists in time, or is it destroyed by<br \/>the external force?<br \/>The aim of this thesis is to introduce a universally valid and mathematically precise<br \/>formalism of the concept of superoscillationslationen, which in particular covers all<br \/>the existing results of the past literature. Moreover, a method is developed which<br \/>ensures the time persistence of superoscillations for whole classes of potentials.<\/p>\n","protected":false},"featured_media":42176,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_acf_changed":false},"product_brand":[],"product_cat":[1630],"product_tag":[3834],"class_list":{"0":"post-42175","1":"product","2":"type-product","3":"status-publish","4":"has-post-thumbnail","6":"product_cat-mathematik-physik-und-geodaesie","7":"product_tag-superoscillations-time-dependent-schroedinger-equation-greens-functions","8":"autor-peter-schlosser","9":"reihe-monographic-series-tu-graz","10":"reihe-monographic-series-tu-grazcomputation-in-engineering-and-science","12":"first","13":"instock","14":"downloadable","15":"virtual","16":"taxable","17":"product-type-simple"},"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.2 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Superoscillations and their Schr\u00f6dinger time evolution - Verlag der TU Graz<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/www.tugraz-verlag.at\/en\/gesamtverzeichnis\/mathematik-physik-und-geodaesie\/superoscillations-and-their-schroedinger-time-evolution-ebook\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Superoscillations and their Schr\u00f6dinger time evolution - Verlag der TU Graz\" \/>\n<meta property=\"og:description\" content=\"Superoscillations are functions with the paradoxical behavior of oscillating (at leastlocally) faster than their largest Fourier component. For example, plane waves withsmall frequencies (e.g. red light) can interfere in such a way that a resulting wavewith arbitrary large frequency is created (e.g. blue light or theoretically even a gammaray).Due to the wave-particle duality in quantum mechanics, also particles can exhibitthis superoscillatory behavior. One of the main questions in this context then is:What happens when a particle with a superoscillating wave function interacts with apotential? Does this delicate interference effect persists in time, or is it destroyed bythe external force?The aim of this thesis is to introduce a universally valid and mathematically preciseformalism of the concept of superoscillationslationen, which in particular covers allthe existing results of the past literature. 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