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1.13 A one-particle, one-dimensional system has the state function = (sin ar) (2/mc²)¹/4²¹² + (cos at) (32/mc)¹/4xx²/² where a is a constant and c = 2.000 A. If the particle's position is measured at r = 0, estimate the probability that the result will lie between 2.000 Å and 2.001 A.

1.13 A one-particle, one-dimensional system has the state function = (sin ar) (2/mc²)¹/4²¹² + (cos at) (32/mc)¹/4xx²/² where a is a constant and c = 2.000 A. If the particle's position is measured at r = 0, estimate the probability that the result will lie between 2.000 Å and 2.001 A.

Physical Chemistry
Physical Chemistry
2nd Edition
ISBN:9781133958437
Author:Ball, David W. (david Warren), BAER, Tomas
Publisher:Ball, David W. (david Warren), BAER, Tomas
Chapter10: Introduction To Quantum Mechanics
Section: Chapter Questions
Problem 10.35E: For an unbound or free particle having mass m in the complete absence of any potential energy that...
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answer 1.13

ability that the result (a) lies between 0.9000 nm and 0.9001 nm (treat this interval as infini- tesimal); (b) lies between 0 and 2 nm (use the table of integrals in the Appendix, if necessary). (c) For what value of x is the probability density a minimum? (There is no need to use calculus to answer this.) (d) Verify that is normalized. 1.13 A one-particle, one-dimensional system has the state function = (sin at) (2/mc²) ¹/4-²¹/² + (cos at) (32/mc) ¹/4xe-x²³/² where a is a constant and c = 2.000 A. If the particle's position is measured at t = 0, estimate the probability that the result will lie between 2.000 Å and 2.001 A. 1.14 Use Eq. (1.23) to find the answer to part (a) of the example at the end of Section 1.6 and compare it with the approximate answer found in the example. 1.15 Which of the following functions meet all the requirements of a probability-density function
Transcribed Image Text:ability that the result (a) lies between 0.9000 nm and 0.9001 nm (treat this interval as infini- tesimal); (b) lies between 0 and 2 nm (use the table of integrals in the Appendix, if necessary). (c) For what value of x is the probability density a minimum? (There is no need to use calculus to answer this.) (d) Verify that is normalized. 1.13 A one-particle, one-dimensional system has the state function = (sin at) (2/mc²) ¹/4-²¹/² + (cos at) (32/mc) ¹/4xe-x²³/² where a is a constant and c = 2.000 A. If the particle's position is measured at t = 0, estimate the probability that the result will lie between 2.000 Å and 2.001 A. 1.14 Use Eq. (1.23) to find the answer to part (a) of the example at the end of Section 1.6 and compare it with the approximate answer found in the example. 1.15 Which of the following functions meet all the requirements of a probability-density function
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