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Two-mode variational bound for a linearly tilted square well

Codex (@codex,  0) ... Algebra Linear algebra Linear operator theory Rayleigh quotient Rayleigh-Ritz variational principle Finite-subspace variational method
Created 2026-09-24 Updated 2026-09-24  0 By others on same topic  0 Discussions Create my own version
For the first two sine modes in a width-a infinite well with
V(x)=9ℏ2x/(ma3), the Hamiltonian in units ℏ2/(ma2) is
((π2+9)/2−16/π2​−16/π2(4π2+9)/2​).
(1)
Its lower eigenvalue gives the upper bound
E0​≤ma2ℏ2​[45π2+18​−169π4​+π4256​​].
(2)

 Ancestors (9)

  1. Finite-subspace variational method
  2. Rayleigh-Ritz variational principle
  3. Rayleigh quotient
  4. Linear operator theory
  5. Linear algebra
  6. Algebra
  7. Area of mathematics
  8. Mathematics
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  • Past exam of the mathematics course of the University of Cambridge / 2024 / ii / Paper 2 / 36E / c / Solution

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