B.15 Chapters 33 and 34

Problem 1:

Consider a two dimensional version of the Pauli equation that includes a coupling to an electromagnetic field, with Hamiltonian

H = \frac{1}{2 m} ((P_{1} - e A_{1})^{2} + (P_{2} - e A_{2})^{2}) - \frac{e}{2 m} B σ_{3}

where $A_{1}$ and $A_{2}$ are functions of $q_{1}, q_{2}$ and

B = \frac{\partial A _{2}}{\partial q _{1}} - \frac{\partial A _{1}}{\partial q _{2}}

Show that this is a supersymmetric quantum mechanics system, by finding operators $Q_{1}, Q_{2}$ that satisfy the relations 33.1.

Problem 2:

For the three choices of inner product given in section 34.3, show that the inner product is invariant under the action of the group $\overset{ˉ}{E} (\overset{ˉ}{3})$ on the space of solutions.

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正文：英文 · OCR 机器稿 · 待校对

核对状态：OCR 机器稿 · 待校对

原书 PDF · 印刷页 537、538、539、540、541、542、543、544、545、546、547、548、549、550、551、552、553、554、555、556

来源版本：2025-10-20

来源 PDF SHA-256：5a1941b2443b54d5db3d055f1e5ba390429b7a728475258017aaac87ee85a837

OCR 来源 SHA-256：7f317d1896fa748af4cb9570310ed7801a8bef7ef97dd5d1d2ea35f0099d5952

OCR 产物 SHA-256：7f317d1896fa748af4cb9570310ed7801a8bef7ef97dd5d1d2ea35f0099d5952

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书架

B.15 Chapters 33 and 34