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The eigenfunctions of a particle in a cubic box with potential V = 0 in the region 0 ≤ x ≤ L, 0 ≤ y ≤ Land 0 ≤ z ≤ L and V = ∞ outside Which of the following functions is also an are denoted as Ψnxnynx. Which of the following functions is also an eigenfunction of the Hamiltonian?
  • a)
    ϕ1 = Ψ123 - Ψ312
  • b)
    ϕ2 = Ψ111 - Ψ222
  • c)
    ϕ3 = Ψ121 - Ψ122
  • d)
    ϕ4 = Ψ212 - Ψ113
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
The eigenfunctions of a particle in a cubic box with potential V = 0 i...
  • The energy of eigenfunctions of a particle in a cubic box must be identical or the same in energy in order to combine with each other.
  • In case of wavefunction Ψ123, the energy will be
  • While, in case of wavefunction Ψ312, the energy will be
  • Thus, the energy of wavefunction Ψ312 and wavefunction Ψ123 are identical.
  • Thus, the function which is also an eigenfunction of the Hamiltonian will be
ϕ1 = Ψ123 - Ψ312
as, Ψ312 and Ψ123 has identical energies.
Hence, the function which is also an eigenfunction of the Hamiltonian will be ϕ1 = Ψ123 - Ψ312
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The eigenfunctions of a particle in a cubic box with potential V = 0 in the region 0 ≤ x ≤ L, 0 ≤ y ≤ Land 0 ≤ z≤ L and V = ∞ outside Which of the following functions is also an are denoted asΨnxnynx. Which of the following functions is also an eigenfunction of the Hamiltonian?a)1=Ψ123-Ψ312b)2=Ψ111-Ψ222c)3=Ψ121-Ψ122d)4=Ψ212-Ψ113Correct answer is option 'A'. Can you explain this answer?
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The eigenfunctions of a particle in a cubic box with potential V = 0 in the region 0 ≤ x ≤ L, 0 ≤ y ≤ Land 0 ≤ z≤ L and V = ∞ outside Which of the following functions is also an are denoted asΨnxnynx. Which of the following functions is also an eigenfunction of the Hamiltonian?a)1=Ψ123-Ψ312b)2=Ψ111-Ψ222c)3=Ψ121-Ψ122d)4=Ψ212-Ψ113Correct answer is option 'A'. Can you explain this answer? for UGC NET 2024 is part of UGC NET preparation. The Question and answers have been prepared according to the UGC NET exam syllabus. Information about The eigenfunctions of a particle in a cubic box with potential V = 0 in the region 0 ≤ x ≤ L, 0 ≤ y ≤ Land 0 ≤ z≤ L and V = ∞ outside Which of the following functions is also an are denoted asΨnxnynx. Which of the following functions is also an eigenfunction of the Hamiltonian?a)1=Ψ123-Ψ312b)2=Ψ111-Ψ222c)3=Ψ121-Ψ122d)4=Ψ212-Ψ113Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for UGC NET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The eigenfunctions of a particle in a cubic box with potential V = 0 in the region 0 ≤ x ≤ L, 0 ≤ y ≤ Land 0 ≤ z≤ L and V = ∞ outside Which of the following functions is also an are denoted asΨnxnynx. Which of the following functions is also an eigenfunction of the Hamiltonian?a)1=Ψ123-Ψ312b)2=Ψ111-Ψ222c)3=Ψ121-Ψ122d)4=Ψ212-Ψ113Correct answer is option 'A'. Can you explain this answer?.
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