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Consider the solutions to particle in one dimensional box of length, L.
Which of the following is true for the group of functions  ψ2(x)
  • a)
    They form a complete set 
  • b)
    They are mutually orthogonal 
  • c)
    As we go up in energy, each successive state has one more node. i.e. ψ1(x) has none, ψ2(x) has one, ψ3(x)  has 2 and so on 
  • d)
    They are alternately even and odd with respect to the centre of the well
Correct answer is option 'A,B,C,D'. Can you explain this answer?
Verified Answer
Consider the solutions to particle in one dimensional box of length,L....
The solution of a symmetric infinite potential well consists of 

Now, any function can be written as a linear combination of these functions (sin and cos)
 They form a complete let
The correct answers are: They are alternately even and odd with respect to the centre of the well, As we go up in energy, each successive state has one more node. i.e.  ψ1(x) has none, ψ2(x) has one, ψ3(x) has 2 and so on, They are mutually orthogonal, They form a complete set
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Most Upvoted Answer
Consider the solutions to particle in one dimensional box of length,L....
The solution of a symmetric infinite potential well consists of 

Now, any function can be written as a linear combination of these functions (sin and cos)
 They form a complete let
The correct answers are: They are alternately even and odd with respect to the centre of the well, As we go up in energy, each successive state has one more node. i.e.  ψ1(x) has none, ψ2(x) has one, ψ3(x) has 2 and so on, They are mutually orthogonal, They form a complete set
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Consider the solutions to particle in one dimensional box of length,L.Which of the following is true for the group of functionsψ2(x)a)They form a complete setb)They are mutually orthogonalc)As we go up in energy, each successive state has one more node.i.e.ψ1(x) has none,ψ2(x)has one,ψ3(x) has 2 and so ond)They are alternately even and odd with respect to the centre of the wellCorrect answer is option 'A,B,C,D'. Can you explain this answer?
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Consider the solutions to particle in one dimensional box of length,L.Which of the following is true for the group of functionsψ2(x)a)They form a complete setb)They are mutually orthogonalc)As we go up in energy, each successive state has one more node.i.e.ψ1(x) has none,ψ2(x)has one,ψ3(x) has 2 and so ond)They are alternately even and odd with respect to the centre of the wellCorrect answer is option 'A,B,C,D'. Can you explain this answer? for Physics 2024 is part of Physics preparation. The Question and answers have been prepared according to the Physics exam syllabus. Information about Consider the solutions to particle in one dimensional box of length,L.Which of the following is true for the group of functionsψ2(x)a)They form a complete setb)They are mutually orthogonalc)As we go up in energy, each successive state has one more node.i.e.ψ1(x) has none,ψ2(x)has one,ψ3(x) has 2 and so ond)They are alternately even and odd with respect to the centre of the wellCorrect answer is option 'A,B,C,D'. Can you explain this answer? covers all topics & solutions for Physics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider the solutions to particle in one dimensional box of length,L.Which of the following is true for the group of functionsψ2(x)a)They form a complete setb)They are mutually orthogonalc)As we go up in energy, each successive state has one more node.i.e.ψ1(x) has none,ψ2(x)has one,ψ3(x) has 2 and so ond)They are alternately even and odd with respect to the centre of the wellCorrect answer is option 'A,B,C,D'. Can you explain this answer?.
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