[{"@context":"http:\/\/schema.org\/","@type":"BlogPosting","@id":"https:\/\/wiki.edu.vn\/all2en\/wiki14\/ortsoperator-wikipedia\/#BlogPosting","mainEntityOfPage":"https:\/\/wiki.edu.vn\/all2en\/wiki14\/ortsoperator-wikipedia\/","headline":"Ortsoperator \u2013 Wikipedia","name":"Ortsoperator \u2013 Wikipedia","description":"before-content-x4 The Orts operator In quantum mechanics belong to the local measurement of particles. after-content-x4 The physical condition \u03a6 {displaystyle","datePublished":"2021-08-27","dateModified":"2021-08-27","author":{"@type":"Person","@id":"https:\/\/wiki.edu.vn\/all2en\/wiki14\/author\/lordneo\/#Person","name":"lordneo","url":"https:\/\/wiki.edu.vn\/all2en\/wiki14\/author\/lordneo\/","image":{"@type":"ImageObject","@id":"https:\/\/secure.gravatar.com\/avatar\/44a4cee54c4c053e967fe3e7d054edd4?s=96&d=mm&r=g","url":"https:\/\/secure.gravatar.com\/avatar\/44a4cee54c4c053e967fe3e7d054edd4?s=96&d=mm&r=g","height":96,"width":96}},"publisher":{"@type":"Organization","name":"Enzyklop\u00e4die","logo":{"@type":"ImageObject","@id":"https:\/\/wiki.edu.vn\/wiki4\/wp-content\/uploads\/2023\/08\/download.jpg","url":"https:\/\/wiki.edu.vn\/wiki4\/wp-content\/uploads\/2023\/08\/download.jpg","width":600,"height":60}},"image":{"@type":"ImageObject","@id":"https:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/f5471531a3fe80741a839bc98d49fae862a6439a","url":"https:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/f5471531a3fe80741a839bc98d49fae862a6439a","height":"","width":""},"url":"https:\/\/wiki.edu.vn\/all2en\/wiki14\/ortsoperator-wikipedia\/","wordCount":5887,"articleBody":"     (adsbygoogle = window.adsbygoogle || []).push({});before-content-x4The Orts operator In quantum mechanics belong to the local measurement of particles.        (adsbygoogle = window.adsbygoogle || []).push({});after-content-x4The physical condition \u03a6 {displaystyle Psi } A particle is mathematically given in quantum mechanics by the associated vector of a Hilbert dream H . This condition is consequently in the BRA-KET notation by the vector | \u03a6 \u27e9 {displaystyle |Psi rangle } described. The observables are opened by self -cubs H shown.        (adsbygoogle = window.adsbygoogle || []).push({});after-content-x4The local operator in particular is the summary of the three observable x^= ( x^1, x^2, x^3) {displaystyle {hat {mathbf {x} }}=({hat {x}}_{1},{hat {x}}_{2},{hat {x}}_{3})} , so that AND ( x^j) = \u27e8x^j\u03a8,\u03a8\u27e9H , j = first , 2 , 3 {Displastyle E ({Hat {x}} _ {j}) = {langle {Hat {x}} _ {j}, psi, psi, psi row} _ {mathrm {h}}, quad j = 1,2,3 } The mean (expectation value) of the measurement results of the J-Ten location coordinate of the particle in the state        (adsbygoogle = window.adsbygoogle || []).push({});after-content-x4\u03a6 {displaystyle Psi } is. [x^j,p^k]=i\u210f\u03b4jk\u00a0,[x^j,x^k]=0=[p^j,p^k]\u00a0,j,k\u2208{1,2,3}{Displaystyle [{has {x}} _ {j}, {has {p}} _ {k}] = mathrm {i}, hbar, delta _ {jk}, quad [{has {x}} _ {j }, {has {x} _ {k}] = 0 = [{has {p}} _ {j}, {has {p}} _ {k}], quad j, kin {1,2,3 }} It follows that the three local coordinates are measurable together and that their spectrum (area of \u200b\u200bthe possible Measured values ) from all over the room R3{displaystyle mathbb {R} ^{3}} consists. The possible places are not quantized, but continuously. Local representation [ Edit | Edit the source text ] The local presentation is defined by the spectral presentation of the local operator. The Hilbertraum H = L 2( R3; C ) {displaystyle H=L^{2}(mathbb {R} ^{3};mathbb {C} )} Is the space of the square integrable complex functions of the local area R3{displaystyle mathbb {R} ^{3}} , every condition \u03a6 {displaystyle Psi } Is through a local wave function \u03a6 ( x ) {displaystyle psi (mathbf {x} )} given. The local operators x^= ( x^1, x^2, x^3) {displaystyle {hat {mathbf {x} }}=({hat {x}}_{1},{hat {x}}_{2},{hat {x}}_{3})} are the The multiplication operator With the coordinate functions, i.e. H. The local operator x^j{displaystyle {hat {x}}_{j}} acts on local wave functions \u03a6 ( x ) {displaystyle psi (mathbf {x} )} By multiplication of the wave function to the coordinate function x j{displaystyle x_{j}}  (x^j\u03c8)(x)=xj\u22c5\u03c8(x){DisplayStyle ({Hat {x}} _ {j}, psi) (mathbf {x}) = x_ {j} cdot psi (mathbf {x})} This operator x^j{displaystyle {hat {x}}_{j}} Is a multiplication operatorA densely defined operator and completed.He is on the underground D = { \u03a6 \u2208 H | x \u22c5 \u03a6 \u2208 H } {displaystyle D={psi in H,|,xcdot psi in H}} defined that lies in h. The expectation value is E(x^j)=\u27e8x^j\u03a8,\u03a8\u27e9L2=\u222bR3xj\u03c8(x)\u03c8(x)\u00afdx=\u222bR3xj|\u03c8(x)|2dx{Displastyle e ({Hat {x}} _ {j}) = {langle {Hat {x}} _ {j}, psi, psi, psi, psi, psi, psi rusle} _ {l^{2}} = int _ {mathbb {r} ^{3}} x_ {j}, psi (mathbf {x}), {overline {psi (mathbf {x})}}, mathrm {d} x = int _ {mathbb {r} ^{3}} x_ {J}, | Psi (Mathbf {x}) |^{2} Mathrm {d} x} The impulse operator acts as a differential operator on local wave functions (if the phases are suitable): (p^k\u03c8)(x)=\u2212i\u210f\u2202\u2202xk\u03c8(x){displaystyle {bigl (}{hat {p}}_{k}psi {bigr )}(mathbf {x} )=-mathrm {i} ,hbar ,{frac {partial }{partial x_{k}}}psi (mathbf {x} )} Self -functions [ Edit | Edit the source text ] The own functions of the local operator must (x^\u03c8x0)(x)=x0\u22c5\u03c8x0(x){displaystyle ({hat {x}}, psi _ {mathbf {x_ {0}}}) (mathbf {x}) = mathbf {x_ {0}} cdot psi _ {mathbf {x_ {0}}} (mathbf {X})} fulfill, whereby \u03a6 x0( x ) {displaystyle psi _{mathbf {x_{0}} }(mathbf {x} )} The own function of the local operator to the eigenvalon x0{displaystyle mathbf {x_{0}} } represent. The own functions \u03a6 ( x0) {displaystyle psi (mathbf {x_{0}} )} Delta distributions correspond to the local operator: x^d ( x – x0) = x0d ( x – x0) {displaystyle {hat {mathbf {x}}} delta (mathbf {x} -mathbf {x_ {0}}) = mathbf {x_ {0}} delta (mathbf {x} -mathbf {x_ {0}})}}}}  With identity: f ( x ) d ( x – x 0) = f ( x 0) d ( x – x 0) {displaystyle f(x)delta (x-x_{0})=f(x_{0})delta (x-x_{0})}  Impulse presentation [ Edit | Edit the source text ] In the impulse presentation, the pulse operator has a multiplicative effect on impulse wave functions \u03c8~( p ) {Displaystyle {tilde {psi}} (mathbf {p})}  (p^k\u03c8~)(p)=pk\u22c5\u03c8~(p){displaystyle ({hat {p}} _ {k}, {tilde {psi}}) (mathbf {p}) = p_ {k} cdot {tilde {psi}} (mathbf {p})} and the local operator as a differential operator: (x^j\u03c8~)(p)=i\u210f\u2202\u2202pj\u03c8~(p){hat {x}} _ {{j} {tilde {psi}}) (Math} {psi) = {PSI) = Mathrm {}, HBAR, {frac {partial} {partial p_ {}}} {tilde {}} (MathBF {P})}       (adsbygoogle = window.adsbygoogle || []).push({});after-content-x4"},{"@context":"http:\/\/schema.org\/","@type":"BreadcrumbList","itemListElement":[{"@type":"ListItem","position":1,"item":{"@id":"https:\/\/wiki.edu.vn\/all2en\/wiki14\/#breadcrumbitem","name":"Enzyklop\u00e4die"}},{"@type":"ListItem","position":2,"item":{"@id":"https:\/\/wiki.edu.vn\/all2en\/wiki14\/ortsoperator-wikipedia\/#breadcrumbitem","name":"Ortsoperator \u2013 Wikipedia"}}]}]