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In any arbitrary potential, an acceptable solution of the Schrodinger equations must satisfy which of the following properties?
- a)The gradient should also be bounded at large distances
- b)The gradient of the solution must be single valued, finite and continuous at the every point
- c)The wave function must vanish at the point where the potential approaches infinity
- d)The wave function must be continuous throughout
Correct answer is option 'A,B,C,D'. Can you explain this answer?
Verified Answer
In any arbitrary potential, an acceptable solution of the Schrodinger ...
The correct answers are: The gradient of the solution must be single valued, finite and continuous at the every point, The gradient should also be bounded at large distances, The wave function must be continuous throughout, The wave function must vanish at the point where the potential approaches infinity
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In any arbitrary potential, an acceptable solution of the Schrodinger ...
Solution:
To understand why all the properties A, B, C, and D must be satisfied by an acceptable solution of the Schrodinger equation in any arbitrary potential, let's discuss each property in detail.
a) The gradient should also be bounded at large distances:
The wave function represents the probability amplitude of finding a particle in a given state. For a physically meaningful solution, the wave function must be well-behaved and finite everywhere, including at large distances. If the gradient of the wave function were not bounded at large distances, it would imply unphysical behaviors such as infinite probabilities or non-normalizable wave functions. Therefore, the gradient of the solution should also be bounded at large distances.
b) The gradient of the solution must be single valued, finite, and continuous at every point:
The gradient of the wave function represents the momentum or velocity of the particle. As a physical quantity, the momentum must be well-defined and finite. Any singularities or discontinuities in the gradient would lead to unphysical behaviors of the particle. Thus, the gradient of the solution must be single valued, finite, and continuous at every point.
c) The wave function must vanish at the point where the potential approaches infinity:
In quantum mechanics, the wave function describes the behavior of a particle in the presence of a potential. As the potential approaches infinity, it implies a region where the particle cannot exist due to an infinitely high barrier. Therefore, the wave function must vanish at such points, indicating that the probability of finding the particle in that region is zero.
d) The wave function must be continuous throughout:
The wave function represents a physical quantity, namely the probability amplitude. For the probability to be well-defined, the wave function must be continuous throughout the entire domain. Any discontinuities could lead to unphysical behaviors, such as infinite probabilities or non-normalizable wave functions. Hence, the wave function must be continuous.
Summary:
In summary, an acceptable solution of the Schrodinger equation in any arbitrary potential must satisfy all the properties A, B, C, and D. These properties ensure that the wave function and its gradient are well-behaved, physically meaningful, and consistent with the principles of quantum mechanics. Violation of any of these properties would lead to unphysical results and is not acceptable in the context of quantum mechanics.
To understand why all the properties A, B, C, and D must be satisfied by an acceptable solution of the Schrodinger equation in any arbitrary potential, let's discuss each property in detail.
a) The gradient should also be bounded at large distances:
The wave function represents the probability amplitude of finding a particle in a given state. For a physically meaningful solution, the wave function must be well-behaved and finite everywhere, including at large distances. If the gradient of the wave function were not bounded at large distances, it would imply unphysical behaviors such as infinite probabilities or non-normalizable wave functions. Therefore, the gradient of the solution should also be bounded at large distances.
b) The gradient of the solution must be single valued, finite, and continuous at every point:
The gradient of the wave function represents the momentum or velocity of the particle. As a physical quantity, the momentum must be well-defined and finite. Any singularities or discontinuities in the gradient would lead to unphysical behaviors of the particle. Thus, the gradient of the solution must be single valued, finite, and continuous at every point.
c) The wave function must vanish at the point where the potential approaches infinity:
In quantum mechanics, the wave function describes the behavior of a particle in the presence of a potential. As the potential approaches infinity, it implies a region where the particle cannot exist due to an infinitely high barrier. Therefore, the wave function must vanish at such points, indicating that the probability of finding the particle in that region is zero.
d) The wave function must be continuous throughout:
The wave function represents a physical quantity, namely the probability amplitude. For the probability to be well-defined, the wave function must be continuous throughout the entire domain. Any discontinuities could lead to unphysical behaviors, such as infinite probabilities or non-normalizable wave functions. Hence, the wave function must be continuous.
Summary:
In summary, an acceptable solution of the Schrodinger equation in any arbitrary potential must satisfy all the properties A, B, C, and D. These properties ensure that the wave function and its gradient are well-behaved, physically meaningful, and consistent with the principles of quantum mechanics. Violation of any of these properties would lead to unphysical results and is not acceptable in the context of quantum mechanics.
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In any arbitrary potential, an acceptable solution of the Schrodinger equations must satisfy which of the following properties?a)The gradient should also be bounded at large distancesb)The gradient of the solution must be single valued, finite and continuous at the every pointc)The wave function must vanish at the point where the potential approaches infinityd)The wave function must be continuous throughoutCorrect answer is option 'A,B,C,D'. Can you explain this answer?
Question Description
In any arbitrary potential, an acceptable solution of the Schrodinger equations must satisfy which of the following properties?a)The gradient should also be bounded at large distancesb)The gradient of the solution must be single valued, finite and continuous at the every pointc)The wave function must vanish at the point where the potential approaches infinityd)The wave function must be continuous throughoutCorrect 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 In any arbitrary potential, an acceptable solution of the Schrodinger equations must satisfy which of the following properties?a)The gradient should also be bounded at large distancesb)The gradient of the solution must be single valued, finite and continuous at the every pointc)The wave function must vanish at the point where the potential approaches infinityd)The wave function must be continuous throughoutCorrect 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 In any arbitrary potential, an acceptable solution of the Schrodinger equations must satisfy which of the following properties?a)The gradient should also be bounded at large distancesb)The gradient of the solution must be single valued, finite and continuous at the every pointc)The wave function must vanish at the point where the potential approaches infinityd)The wave function must be continuous throughoutCorrect answer is option 'A,B,C,D'. Can you explain this answer?.
In any arbitrary potential, an acceptable solution of the Schrodinger equations must satisfy which of the following properties?a)The gradient should also be bounded at large distancesb)The gradient of the solution must be single valued, finite and continuous at the every pointc)The wave function must vanish at the point where the potential approaches infinityd)The wave function must be continuous throughoutCorrect 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 In any arbitrary potential, an acceptable solution of the Schrodinger equations must satisfy which of the following properties?a)The gradient should also be bounded at large distancesb)The gradient of the solution must be single valued, finite and continuous at the every pointc)The wave function must vanish at the point where the potential approaches infinityd)The wave function must be continuous throughoutCorrect 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 In any arbitrary potential, an acceptable solution of the Schrodinger equations must satisfy which of the following properties?a)The gradient should also be bounded at large distancesb)The gradient of the solution must be single valued, finite and continuous at the every pointc)The wave function must vanish at the point where the potential approaches infinityd)The wave function must be continuous throughoutCorrect answer is option 'A,B,C,D'. Can you explain this answer?.
Solutions for In any arbitrary potential, an acceptable solution of the Schrodinger equations must satisfy which of the following properties?a)The gradient should also be bounded at large distancesb)The gradient of the solution must be single valued, finite and continuous at the every pointc)The wave function must vanish at the point where the potential approaches infinityd)The wave function must be continuous throughoutCorrect answer is option 'A,B,C,D'. Can you explain this answer? in English & in Hindi are available as part of our courses for Physics.
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