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A free particle is moving in positive direction with a linear momentum 'V' . The wave function of the particle normalized in a length '(1)/(sqrtL)e^(ip//ℏ)x' is '(1)/(sqrtL)e^(-ip//ℏ)x' '(1)/(sqrtL)cos (p)/(ℏ)x' '(1)/(sqrtL)sin (p)/(ℏ)x' 'L' 'p'?
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A free particle is moving in positive direction with a linear momentum...
Explanation of Free Particle Wave Function:
The wave function of a free particle moving in the positive direction with linear momentum 'p' can be expressed as:
Normalized wave function:
- The normalized wave function of the particle in a length 'L' is given by:
- φ(x) = (1/√L)e^(ipx/ℏ)
Options for the wave function:
- The given options are:
- φ(x) = (1/√L)e^(-ipx/ℏ)
- φ(x) = (1/√L)cos(px/ℏ)
- φ(x) = (1/√L)sin(px/ℏ)
Explanation of options:
- The correct wave function is φ(x) = (1/√L)e^(-ipx/ℏ) as given in the second option.
- This wave function represents a free particle moving in the positive direction with linear momentum 'p'.
Understanding the wave function:
- The wave function describes the probability amplitude of finding the particle at a given position x.
- The normalization factor (1/√L) ensures that the total probability of finding the particle over the entire length 'L' is equal to 1.
Conclusion:
- The correct wave function for a free particle moving in the positive direction with linear momentum 'p' is φ(x) = (1/√L)e^(-ipx/ℏ), as given in the second option.
The wave function of a free particle moving in the positive direction with linear momentum 'p' can be expressed as:
Normalized wave function:
- The normalized wave function of the particle in a length 'L' is given by:
- φ(x) = (1/√L)e^(ipx/ℏ)
Options for the wave function:
- The given options are:
- φ(x) = (1/√L)e^(-ipx/ℏ)
- φ(x) = (1/√L)cos(px/ℏ)
- φ(x) = (1/√L)sin(px/ℏ)
Explanation of options:
- The correct wave function is φ(x) = (1/√L)e^(-ipx/ℏ) as given in the second option.
- This wave function represents a free particle moving in the positive direction with linear momentum 'p'.
Understanding the wave function:
- The wave function describes the probability amplitude of finding the particle at a given position x.
- The normalization factor (1/√L) ensures that the total probability of finding the particle over the entire length 'L' is equal to 1.
Conclusion:
- The correct wave function for a free particle moving in the positive direction with linear momentum 'p' is φ(x) = (1/√L)e^(-ipx/ℏ), as given in the second option.
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A free particle is moving in positive direction with a linear momentum 'V' . The wave function of the particle normalized in a length '(1)/(sqrtL)e^(ip//ℏ)x' is '(1)/(sqrtL)e^(-ip//ℏ)x' '(1)/(sqrtL)cos (p)/(ℏ)x' '(1)/(sqrtL)sin (p)/(ℏ)x' 'L' 'p'?
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A free particle is moving in positive direction with a linear momentum 'V' . The wave function of the particle normalized in a length '(1)/(sqrtL)e^(ip//ℏ)x' is '(1)/(sqrtL)e^(-ip//ℏ)x' '(1)/(sqrtL)cos (p)/(ℏ)x' '(1)/(sqrtL)sin (p)/(ℏ)x' 'L' 'p'? for Chemistry 2024 is part of Chemistry preparation. The Question and answers have been prepared according to the Chemistry exam syllabus. Information about A free particle is moving in positive direction with a linear momentum 'V' . The wave function of the particle normalized in a length '(1)/(sqrtL)e^(ip//ℏ)x' is '(1)/(sqrtL)e^(-ip//ℏ)x' '(1)/(sqrtL)cos (p)/(ℏ)x' '(1)/(sqrtL)sin (p)/(ℏ)x' 'L' 'p'? covers all topics & solutions for Chemistry 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A free particle is moving in positive direction with a linear momentum 'V' . The wave function of the particle normalized in a length '(1)/(sqrtL)e^(ip//ℏ)x' is '(1)/(sqrtL)e^(-ip//ℏ)x' '(1)/(sqrtL)cos (p)/(ℏ)x' '(1)/(sqrtL)sin (p)/(ℏ)x' 'L' 'p'?.
A free particle is moving in positive direction with a linear momentum 'V' . The wave function of the particle normalized in a length '(1)/(sqrtL)e^(ip//ℏ)x' is '(1)/(sqrtL)e^(-ip//ℏ)x' '(1)/(sqrtL)cos (p)/(ℏ)x' '(1)/(sqrtL)sin (p)/(ℏ)x' 'L' 'p'? for Chemistry 2024 is part of Chemistry preparation. The Question and answers have been prepared according to the Chemistry exam syllabus. Information about A free particle is moving in positive direction with a linear momentum 'V' . The wave function of the particle normalized in a length '(1)/(sqrtL)e^(ip//ℏ)x' is '(1)/(sqrtL)e^(-ip//ℏ)x' '(1)/(sqrtL)cos (p)/(ℏ)x' '(1)/(sqrtL)sin (p)/(ℏ)x' 'L' 'p'? covers all topics & solutions for Chemistry 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A free particle is moving in positive direction with a linear momentum 'V' . The wave function of the particle normalized in a length '(1)/(sqrtL)e^(ip//ℏ)x' is '(1)/(sqrtL)e^(-ip//ℏ)x' '(1)/(sqrtL)cos (p)/(ℏ)x' '(1)/(sqrtL)sin (p)/(ℏ)x' 'L' 'p'?.
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