资源描述：
《量子力学导论第章答案》由会员上传分享，免费在线阅读，更多相关内容在工程资料-天天文库。
1、第四章力学量用算符表达与表象变换4.1）设与为厄米算符，则和也是厄米算符。由此证明，任何一个算符均可分解为，与均为厄米算符，且证：ⅰ）为厄米算符。ⅱ）也为厄米算符。ⅲ）令，则，且定义（1）由ⅰ），ⅱ）得，即和皆为厄米算符。则由（1）式，不难解得4.2）设是的整函数，证明整函数是指可以展开成。证：（1）先证。同理，Riverimplementationcomprehensive,throughbuiltreservoir,andbuiltdike,andretainingdam,andanti-infiltrationgovernance,focuswaterengineering
2、andwaterconnectionengineering,speedupformedlayoutreasonable,ecologicalgood,andintroductionrowproperly,andcyclesmooth,andstoragereliefboth,andFengdrytransfers,andmoresource15现在，而。又而4.3）定义反对易式，证明证：4.4）设，，为矢量算符，和的标积和矢积定义为，为Levi-civita符号，试验证Riverimplementationcomprehensive,throughbuiltreservoir,a
3、ndbuiltdike,andretainingdam,andanti-infiltrationgovernance,focuswaterengineeringandwaterconnectionengineering,speedupformedlayoutreasonable,ecologicalgood,andintroductionrowproperly,andcyclesmooth,andstoragereliefboth,andFengdrytransfers,andmoresource15（1）（2）（3）证：（1）式左端（1）式右端也可以化成。（1）式得证。（2）式
4、左端（）（2）式右端故（2）式成立。（3）式验证可仿（2）式。4.5）设与为矢量算符，为标量算符，证明（1）（2）证：（1）式右端（1）式左端（2）式右端（2）式左端4.6）设是由，构成的标量算符，证明Riverimplementationcomprehensive,throughbuiltreservoir,andbuiltdike,andretainingdam,andanti-infiltrationgovernance,focuswaterengineeringandwaterconnectionengineering,speedupformedlayoutreasona
5、ble,ecologicalgood,andintroductionrowproperly,andcyclesmooth,andstoragereliefboth,andFengdrytransfers,andmoresource15（1）证：（2）（3）同理可证，（4）（5）将式（3）、（4）、（5）代入式（2），于是（1）式得证。4.7）证明。证：利用基本对易式即得。因此其次，由于和对易，所以因此，4.8）证明（1）Riverimplementationcomprehensive,throughbuiltreservoir,andbuiltdike,andretainingd
6、am,andanti-infiltrationgovernance,focuswaterengineeringandwaterconnectionengineering,speedupformedlayoutreasonable,ecologicalgood,andintroductionrowproperly,andcyclesmooth,andstoragereliefboth,andFengdrytransfers,andmoresource15（2）（3）（4）证:（1）利用公式，，有其中因此（2）利用公式，（Δ）可得①②③由①②③，则（2）得证。（3）（4）就此式的一个
7、分量加以证明，由4.4）（2），，其中（即）Riverimplementationcomprehensive,throughbuiltreservoir,andbuiltdike,andretainingdam,andanti-infiltrationgovernance,focuswaterengineeringandwaterconnectionengineering,speedupformedlayoutreasonable,ecologicalgood,andintrod
