{"title":"用量子波阻抗函数重新表述透射和反射问题","authors":"O. Hryhorchak","doi":"10.30970/jps.25.4001","DOIUrl":null,"url":null,"abstract":"On the base of a 1D Shr\\\"{o}dinger equation the non-linear first-order differential equation (Ricatti type) for a quantum wave impedance function was derived. The advantages of this approach were discussed and demonstrated for a case of a single rectangular barrier. Both the scattering and the bound states problem were reformulated in terms of a quantum wave impedance and its application for solving both these problems was considered. The expressions for a reflection and a transmission coefficient were found on the base of a quantum wave impedance approach.","PeriodicalId":43482,"journal":{"name":"Journal of Physical Studies","volume":"150 4 1","pages":""},"PeriodicalIF":0.7000,"publicationDate":"2020-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"10","resultStr":"{\"title\":\"Reformulation of transmission and reflection problems in terms of quantum wave impedance function\",\"authors\":\"O. Hryhorchak\",\"doi\":\"10.30970/jps.25.4001\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"On the base of a 1D Shr\\\\\\\"{o}dinger equation the non-linear first-order differential equation (Ricatti type) for a quantum wave impedance function was derived. The advantages of this approach were discussed and demonstrated for a case of a single rectangular barrier. Both the scattering and the bound states problem were reformulated in terms of a quantum wave impedance and its application for solving both these problems was considered. The expressions for a reflection and a transmission coefficient were found on the base of a quantum wave impedance approach.\",\"PeriodicalId\":43482,\"journal\":{\"name\":\"Journal of Physical Studies\",\"volume\":\"150 4 1\",\"pages\":\"\"},\"PeriodicalIF\":0.7000,\"publicationDate\":\"2020-10-09\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"10\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Physical Studies\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.30970/jps.25.4001\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"PHYSICS, MULTIDISCIPLINARY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Physical Studies","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.30970/jps.25.4001","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"PHYSICS, MULTIDISCIPLINARY","Score":null,"Total":0}
Reformulation of transmission and reflection problems in terms of quantum wave impedance function
On the base of a 1D Shr\"{o}dinger equation the non-linear first-order differential equation (Ricatti type) for a quantum wave impedance function was derived. The advantages of this approach were discussed and demonstrated for a case of a single rectangular barrier. Both the scattering and the bound states problem were reformulated in terms of a quantum wave impedance and its application for solving both these problems was considered. The expressions for a reflection and a transmission coefficient were found on the base of a quantum wave impedance approach.
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