• 2022-07-23
    处于三维各向同性谐振子第一激发态的粒子, 受到微扰 [tex=3.5x1.5]QtA0Z04GgW4d1d+cV/x2rOzIXhVig5ItoITbSyg/CXg=[/tex] 的作用, 式中 [tex=0.643x1.0]+D9NhKovEP8INGz+KZnr1A==[/tex] 为常数, 求能量的一级修正.
  • 解:[tex=24.714x4.429]VO0aNJcu+q/RvsbG1Jqk/8zRXPfufT85Ml23dMsEoLyyjxgGJhrTlZWLWmc+zMbsFEdWMFfzSHWQG3TaXCDyfrChHgcYRakaysg4hcv00iSajdxnGSBrLmw05YvBI6v3QBhvoroq4qaR0WONBI38YjQuH0q7OqCLWtobwxlJ3Ieg9DfLJjr/8lB/gylR5h3uRPEab0m5WyMwmu3hdxNzpEpLgfq8cUsAOTNhQmXs/mX8XjpMstjI9NaDEyZykJxQ1RsTC7ZFBQf941VXZ5NhJsfUljg+LQp08WKlzorzuKZeNnzyeH/M5PVDC/+dXRvliZv2eqwB3EY4dHCpaz0M5c7Bef0c8VePtLT825bSCwE=[/tex][tex=1.214x1.5]T/eIZ3tYct5xRc54NYLz6w==[/tex] 的本征值与本征函数为[tex=21.143x8.643]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[/tex]第一激发态能量 [tex=4.214x1.357]It98wJPNURLmwhXrxFRQ0O2Tkd/bSpRBG5weoJeDnpo=[/tex] 是三度简并的, 相应的波函数为 [tex=24.214x1.357]h+B0TMdCjOl0tBP35f13zipkHakCV9VfEVflVgQ5hNXn8udK0OWDfLhI5h2NnwL6a89obIR/jhWP2Wh2DMMbHJOe4lxpH5PbS4U1BYFK5p4nwo3ioNwp5Lmn/MlJQ5YmcGccejnTVFJuuATWrC+8Y/xfzZ4tPCd0AfdODOvcUw8=[/tex]令零级近似波函数为[tex=11.643x1.571]vhEha/P0dLKRDzobZay9lvl0j/YsRP6lVSTyds0lw8n1H5IxvA1F80Ryap3JyDHTxSmQS5U+nEANmRO8rsH5eIVvD+CThtkve9j3GpTfZ7c=[/tex]系数 [tex=2.357x1.0]UGs/m/TxQmhHsmQOGjDkXNWKwLcoBCSwqBeGHaNqe30=[/tex] 满足方程[tex=24.143x5.214]NeoTBlf1CmkUoMf07Si5dJu6YfdDHu15QbSBXLcR2T5yjVIMa2TU1ts2bKa+yxAwehathBuVDReZbe6H/5aXyfnKX3gHgSXF+yft3zNOegQhdzAtbQV1qZtNngKz89Y3rx9hP+xXPfLQEA3djtrjHsV6JQ1vbLbl5XOQnNEFt3u46W1iMDxyIyc6NrmeTsaaUmM9WLtAQiO8X15beUehDCGxI/A4lRIXOh5lPiHBqiAU86TyWovSYSeqvvSGyi5UnA4T204qkUOUZtlTB2nnWDVdkK6ch8WpCr71YfnATKrdkkOAovegMBPYvBRNdJ64XPHRP8mLEf/ayXZLae8QnbIqDwqGzeHgyFf1vgEcVGeN/h+9M0syHq1+nFo+EehK2SKgkesVvT/AOlxp8II4tc+CLysRmXOWeKnyzOH8r98=[/tex]其中[tex=15.929x2.643]Hd94xy7h2R1k1hh0RT0sehmxPkTeAs4aPHCcSQ47ATPmhleNJL689o5a29kyM7MhBe/GKCp8kvgEQ2/txtoUEKG2CbjBcr6NwTuTN2NIwRtwzaraKZA3uTH/zDwnQmCqQgfgag7KbvYEbYegnW1i+g==[/tex]利用公式[tex=22.0x6.071]matdaI0rgNV4KjKiBn9YZYa5FbyR/OplkWkUp9enLwI0NfMLisAFT+U6K2zl2R+wIIh0b5ODSAjN0FFVXeTuSOBHuMhOdh43k9KbjWmj6ZF2a7pTCvZtQ5EWoHHe0GVGWQ2L+IF8s4WmyWtcMLBH3rRo6DjjE21EOoFaIH9KdnYxOQC4USApDs7I/3vMOkcbGHejh+Xf90PMWdlAPAL+uVsk36RWylzv6lMLNz3hjXg/rKlyJ8KElwlYNvCsIKKP[/tex]算出  [tex=9.357x1.571]hH1w/lFharGEDoRzkrEmTaey7GyVIYzZRTiVKSDcC8QDtFpwSMcOk20DA9JQbCoNng/2JWBKYQsfIkjqE/qdie6t8Vpe19w7wipLbbgZNx0=[/tex]其余 [tex=2.714x1.571]Hd94xy7h2R1k1hh0RT0seiEkhOLcMiwRadmml0u5kTc=[/tex] 将它们代入(8) 式, 得[tex=22.429x5.214]jcCMHflCR8OS9TosV6N5vCmld19eyyIYfDuTvYwTu3tZhU4TH/XhfONFq2OxTDKz3vZamF7pJW9HV7YNXQx5cPUYwmup6qhISap8FA8DBCE0MgicJ58TnWVe1d4zTDpnpWJXJNVMTO6+mNHpSN1ve9xIz+VGqRW5bsqloai1YGsB9/XjovR2x0/WSwe3e9iQWGF0pYlXA7xiRNTcFMWdtpg3gcKQpSI1SKhoeELk1AeHHgpS1rq9lYLsJaBkaRM0So0HQfBXJJgHODNul32mc4Dzn73k4OzcrdQJbg0axzncyWUZhQt4dCjkCtV2hXUkE2TMNwsrxKRmaZG4yxludw==[/tex]解之得[tex=18.5x2.429]CjpsOSkigbuCxvbJl+T13UCshxzDTetRwd/cD3VU5xMMHx5TrCFv266M3kTfUTZoI5oasGb11/K1Lib/uXA217a4W4SgeJpTgE9V9qPCW5lAPjI2vhzMGyhaSLAHMkLgY2W/xMOMMJJKLGLUy2OnQK6rd3MxjeUOMxT8FcrcvtA=[/tex]

    内容

    • 0

      产品[tex=0.857x1.0]N7iCrOsS+NNEUUlnsYCi1g==[/tex]和[tex=0.643x1.0]O+viFNA0oHTwnBtQyi80Zw==[/tex]是互补品。需求函数;[br][/br]$Q_{X}=640-4 P_{X}-P_{Y}, \quad Q_{Y}=\frac{1}{2} Q_{X}-\frac{1}{2} P_{Y}$\ \假定两者短期供给是固定的:[br][/br][tex=7.571x1.214]CfZnuLHqwTFF3JM+8Dj0b8jBQ/cIxAsLu6pTzTLTHBE=[/tex]求:这两种产品的均衡价格为多少?

    • 1

      设随机变量 [tex=0.857x1.0]KGogyvwDAIJf/iL0H/9wjg==[/tex] 与 [tex=0.643x1.0]jDVSpgNhHe+VJmgvx3gg1Q==[/tex] 相互独立,且服从参数为 1 的指数分布. 记 [tex=13.5x1.357]ZrmgIX329+lIMwj+0JP7oX4KmceUiv4NOTdLGvSfjGFY26aIR9qNFK9EJaP3gu/x[/tex] 求[tex=3.857x1.357]t0PsS3YAPSnhTBV9LUFwGQ==[/tex]

    • 2

      设h为X上函数,证明下列两个条件等价,(1)h为一单射(2)对任意X上的函数[tex=5.429x1.214]3BrfPgAFe5dbHQTMAYnbS+118W4YAj6CiW06EKMaxNI=[/tex]蕴涵[tex=1.786x1.214]pxzkG5OdsKT9CiCwC5OvPQ==[/tex]

    • 3

      求下列函数的导函数:(1) [tex=5.0x2.357]X/CieCDGJ7iPQ3YFWuscHxHrcIE/dPFa9tFyiJXze8A=[/tex](2)[tex=6.643x1.714]Oj74y/L+OxY81QME5JWMcl+7PZ2FGQswwvjgVhjq1Dmb6dBU0oAjZBW7eFBVjqo6[/tex]

    • 4

      求柱面 [tex=3.929x1.429]/zgqabtImeIaKGhfpDlfIA==[/tex] 与三张平面 x =0, y = x , z =0 所围的在第一卦限的立体的体积。