The probability that a particle in an infinite square well located in the central one fourth of the well for the quantum state ( n = 1 ) .

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Answer 1

Question

Chapter 35, Problem 48P

(a)

To determine

The probability that a particle in an infinite square well located in the central one fourth of the well for the quantum state (n=1) .

(b)

To determine

The probability that a particle in an infinite square well located in the central one fourth of the well for the quantum state (n=2) .

(c)

To determine

The probability that a particle in an infinite square well located in the central one fourth of the well for the quantum state (n=5) .

(d)

To determine

The probability that a particle in an infinite square well located in the central one fourth of the well for the quantum state (n=20) .

(e)

To determine

The classical probability in this situation.

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A one-dimensional infinite well of length 200 pm contains an electron in its third excited state.We position an electrondetector probe of width 2.00 pm so that it is centered on a point of maximum probability density. (a) What is the probability of detection by the probe? (b) If we insert the probe as described 1000 times, how many times should we expect the electron to materialize on the end of the probe (and thus be detected)?

An electron is trapped in a one-dimensional infinite potential well that is 460 pm wide; the electron is in its ground state. What is the probability that you can detect the electron in an interval of width δx = 5.0 pm centered at x = 300 pm? (Hint: The interval δx is so narrow that you can take the probability density to be constant within it.)

A quantum mechanical particle moving in one dimension between impenetrable barriers has energy levels ϵ,4ϵ,9ϵ,...ϵ, 4⁢ϵ, 9⁢ϵ, ... , that is En=ϵn2En=ϵ n2 . Suppose that ϵ=0.035eVϵ⁢ =0.035⁢ eV for a certain such quantum system. What is the probability (as a percent) that such a system will be in its ground state when it is in contact with a reservoir at room temperature? The probability that the system will be in its ground state when it is in contact with a reservoir at room temperature is

Answer 2

Question

Chapter 35, Problem 48P

(a)

To determine

The probability that a particle in an infinite square well located in the central one fourth of the well for the quantum state (n=1) .

(b)

To determine

The probability that a particle in an infinite square well located in the central one fourth of the well for the quantum state (n=2) .

(c)

To determine

The probability that a particle in an infinite square well located in the central one fourth of the well for the quantum state (n=5) .

(d)

To determine

The probability that a particle in an infinite square well located in the central one fourth of the well for the quantum state (n=20) .

(e)

To determine

The classical probability in this situation.

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Answer 3

Question

Chapter 35, Problem 48P

(a)

To determine

The probability that a particle in an infinite square well located in the central one fourth of the well for the quantum state (n=1) .

(b)

To determine

The probability that a particle in an infinite square well located in the central one fourth of the well for the quantum state (n=2) .

(c)

To determine

The probability that a particle in an infinite square well located in the central one fourth of the well for the quantum state (n=5) .

(d)

To determine

The probability that a particle in an infinite square well located in the central one fourth of the well for the quantum state (n=20) .

(e)

To determine

The classical probability in this situation.

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Answer 4

Question

Chapter 35, Problem 48P

(a)

To determine

The probability that a particle in an infinite square well located in the central one fourth of the well for the quantum state (n=1) .

(b)

To determine

The probability that a particle in an infinite square well located in the central one fourth of the well for the quantum state (n=2) .

(c)

To determine

The probability that a particle in an infinite square well located in the central one fourth of the well for the quantum state (n=5) .

(d)

To determine

The probability that a particle in an infinite square well located in the central one fourth of the well for the quantum state (n=20) .

(e)

To determine

The classical probability in this situation.

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Answer 5

Chapter 35, Problem 48P

(a)

To determine

The probability that a particle in an infinite square well located in the central one fourth of the well for the quantum state (n=1) .

(b)

To determine

The probability that a particle in an infinite square well located in the central one fourth of the well for the quantum state (n=2) .

(c)

To determine

The probability that a particle in an infinite square well located in the central one fourth of the well for the quantum state (n=5) .

(d)

To determine

The probability that a particle in an infinite square well located in the central one fourth of the well for the quantum state (n=20) .

(e)

To determine

The classical probability in this situation.

Answer 6

Chapter 35, Problem 48P

(a)

To determine

The probability that a particle in an infinite square well located in the central one fourth of the well for the quantum state (n=1) .

Answer 7

Chapter 35, Problem 48P

(a)

To determine

The probability that a particle in an infinite square well located in the central one fourth of the well for the quantum state (n=1) .

Answer 8

(b)

To determine

The probability that a particle in an infinite square well located in the central one fourth of the well for the quantum state (n=2) .

Answer 9

(b)

To determine

The probability that a particle in an infinite square well located in the central one fourth of the well for the quantum state (n=2) .

Answer 10

(c)

To determine

The probability that a particle in an infinite square well located in the central one fourth of the well for the quantum state (n=5) .

Answer 11

(c)

To determine

The probability that a particle in an infinite square well located in the central one fourth of the well for the quantum state (n=5) .

Answer 12

(d)

To determine

The probability that a particle in an infinite square well located in the central one fourth of the well for the quantum state (n=20) .

Answer 13

(d)

To determine

The probability that a particle in an infinite square well located in the central one fourth of the well for the quantum state (n=20) .

Answer 14

(e)

To determine

The classical probability in this situation.

Answer 15

(e)

To determine

The classical probability in this situation.

Answer 16

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Answer 17

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Answer 18

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Answer 19

Ch. 35.1 - Prob. 35.1GI Ch. 35.2 - Prob. 35.2GI Ch. 35.3 - Prob. 35.3GI Ch. 35.3 - Prob. 35.4GI Ch. 35.3 - Prob. 35.5GI Ch. 35.4 - Prob. 35.6GI Ch. 35 - Prob. 1FTD Ch. 35 - Prob. 2FTD Ch. 35 - Prob. 3FTD Ch. 35 - Prob. 4FTD

The probability that a particle in an infinite square well located in the central one fourth of the well for the quantum state ( n = 1 ) .

Solution Summary: The author explains the probability of finding the particle in a given region for any value of n.

The probability that a particle in an infinite square well located in the central one fourth of the well for the quantum state (n=1) .

The probability that a particle in an infinite square well located in the central one fourth of the well for the quantum state (n=2) .

The probability that a particle in an infinite square well located in the central one fourth of the well for the quantum state (n=5) .

The probability that a particle in an infinite square well located in the central one fourth of the well for the quantum state (n=20) .

The classical probability in this situation.

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Chapter 35 Solutions