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First of all, for any operator A, we can define its adjoint, A-dagger, via this equation. The idea behind this is, that...","preview":{"posterSrc":"//avatars.mds.yandex.net/get-vthumb/2461135/474f8ab04edd0baea9ed95e2abf5c354/564x318_1","videoSrc":"https://video-preview.s3.yandex.net/kNIIVQEAAAA.mp4","videoType":"video/mp4"},"target":"_self","position":"13","reqid":"1774857300389892-144805137164126993-balancer-l7leveler-kubr-yp-klg-208-BAL","summary":{"fullTextUrl":"/int_search_summary?data=http%3A%2F%2Fwww.youtube.com%2Fwatch%3Fv%3DVPbIjwslxiw","linkTemplate":"/video/preview/16248126731006664545?parent-reqid=1774857300389892-144805137164126993-balancer-l7leveler-kubr-yp-klg-208-BAL&text=Adjoint&t=%%timestamp%%&ask_summarization=1"},"isAdultDoc":false,"relatedParams":{"text":"Adjoint / Daggered Operators in Quantum Mechanics","related_orig_text":"Adjoint","related_porno":false,"related_less_3m_off":true,"client":"d2d","no_cnt":1,"related_src":"serp","related":"{\"porno\":false,\"vfp\":1,\"orig_text\":\"Adjoint\",\"url\":\"http:\\/\\/www.youtube.com\\/watch?v=VPbIjwslxiw\",\"src\":\"serp\",\"rvb\":\"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_E_EBggQkAYAEKyqLARABGniBAwLzA_0DAOz8Av37AAEACwoHAPcBAQDkBf0BAPwCAPMA_v7_AAAAEQH1AQgAAAD2-f__9P8BABAEAfLzAAAABQAD7vsAAAAODf0DEf4BAQMCBwED_wAACf3xCwAAAAAIAgES_wAAAPv_BPgAAAAADv4B9gAAAAAgAC11S947OBNACUhOUAIqhAIQABrwAX_qF_7Y9eUB3CnuALob2f-QPAT__DvLAMQTBP-t9b4BAATrAOvs4AEOCRr_1ADaAEn0wf8Su_X_R-Tk_z6-DQDUAvwBMa_zAUASGwLuBdP_2yc0_fzhAgAXt-kACQ7r_gkCEP7rGur_8hjTAir7NQEPCTIEM_srAdij_QHR6Pn76djT_QAi8fzetBj-BA06_huzCwQi-A778Dnd_BDyCwf-2hv89DDoAwLr-AABAQ737OMECf74-QAwAhYCzAoSCvD1LALR8vkA0_8E-FPv_vvYBvTzC-zzCQj6EATs5wAL9_D17uQCAQrv9wgI4h3Z8CAALb9OADs4E0AJSGFQAipzEAAaYPsIACASF88E2EjV7QbDHN3l5gz_zPn__MH_-ErJ8fUj1anjOQAL6yTzpAAAABOn8hzmALt7yNj5EdlSDM3j2z0Wf9QIRALTPBbKAh82085Q_UAeCAD3Fb8TQxDCbwf4HiAALZb5Ezs4E0AJSG9QAiqvBhAMGqAGAACAQAAAsMEAAFxCAABQwQAAsEEAAODBAACAQAAAOMIAADjCAACAwAAAkMEAAIBBAAAAQQAAhMIAABDBAAAMwgAA2EEAAOBAAACAQAAAoMAAAERCAAAkQgAAkEEAAJDBAABQQQAA4EAAAATCAADQwQAAmkIAAIA_AADQQQAA-EEAAADAAABwwQAA4MAAACxCAAB0wgAAmEIAAABAAADIQQAAOMIAAFBBAAAAQgAAQMAAALBBAAAkQgAAmMEAABjCAACwQQAAyMEAAAzCAACAQQAA-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-QgAAiMEAAJTCAAAAwgAAhsIgADgTQAlIdVABKo8CEAAagAIAAJa-AAAwPQAAUD0AAAQ-AADgPAAATD4AACw-AABbvwAAlr4AADw-AACgPAAAiL0AAEQ-AABsPgAAVL4AABC9AAAUPgAA6D0AAJo-AADiPgAAfz8AAKC8AAB8PgAAuD0AAIq-AAC4PQAAHD4AAGS-AACAuwAAsj4AAJY-AACmvgAAlr4AAAw-AAAcvgAAjj4AADA9AACivgAAkr4AAPK-AAA0vgAAcD0AAIA7AAA0vgAAcD0AAFA9AACSPgAAXL4AAFA9AADSvgAADD4AADy-AADIPQAAED0AAFC9AABwvQAAdT8AAPi9AACAuwAAkj4AALK-AAAEPgAAyD0AAJa-IAA4E0AJSHxQASqPAhABGoACAAA0vgAAjj4AALi9AAAhvwAAir4AACS-AADaPgAAqL0AAKg9AAAEPgAA-D0AAJq-AABwPQAATL4AAMi9AADIvQAAiL0AABc_AADgvAAAjj4AAKI-AAB8vgAAqD0AAEy-AADgvAAAiL0AAOi9AAAsPgAAhj4AADC9AAD4PQAAML0AAEy-AABQvQAAJD4AAAy-AACuPgAALD4AAEy-AACIPQAAAz8AAEA8AABUPgAAQDwAAKi9AACyPgAAf78AADA9AAA0vgAAXD4AAAw-AABMPgAAjj4AAJg9AAAEPgAAcD0AAAy-AADYPQAAiL0AAFy-AABwvQAAyD0AAIA7AABAPCAAOBNACUh8UAEwCTgBSgBgAGgA\"}","related_url":"http://www.youtube.com/watch?v=VPbIjwslxiw","parent-reqid":"1774857300389892-144805137164126993-balancer-l7leveler-kubr-yp-klg-208-BAL","related_vfp":1,"relatedVideo":"yes"},"cwidth":1920,"cheight":1080,"cratio":1.77777,"dups":["16248126731006664545"],"episode":0,"season":0,"isEmbedOnly":false,"greenHost":"YouTube","hasTranslation":true,"contentTypeId":null,"censored":false,"censoredShock":false,"isShockDoc":false,"videoContentId":"2838214794"},"14951891728431501179":{"videoId":"14951891728431501179","docid":"34-7-5-Z32F2245EAD76A4CE","description":"Performing adjoint sensitivity analysis over implicitly given relations requires additional derivative information. 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