9.20 What is the uncertainty in position of a proton that has an uncertainty in velocity of
(a) 10 Å s−^1 , (b) 1 Å s−^1 , and (c) 1000 Å s−^1?
9.21 What is the uncertainty in position of an electron that has an uncertainty in velocity of
(a) 10 Å s−^1 , (b) 1 Å s−^1 , and (c) 1000 Å s−^1?
9.22 What is the uncertainty in position of a 5-g snail that has an uncertainty in velocity of
(a) 10 cm s−^1 , (b) 1cms−^1 , and (c) 1μms−^1?
9.23 Write the quantum operator for (a) momentum, (b) position, and (c) momentum squared.
9.24Write Schrödinger’s equation for the potential V(x) equal to (a) Ax, (b) Ax^2 , and (c) Ax+Bx^2.
9.25 Write Schrödinger’s equation for the potential V(x,y) equal to (a) Ax^3 +By, (b) Ax+By^3 ,
and (c) Axy.
9.26 Write Schrödinger’s equation for the potential V(x,y,z) equal to (a) Ax+By+Cz, (b) Ax^3 +
By+Cz^2 , and (c) Axyz.
9.27 Explain why the observation of a different diffraction for two slits compared to one raises
questions about the nature of a particle.
9.28 Why can both the position and velocity of an object not be determined to high accuracy?
9.29 Consider a one-dimensional problem that yields a wavefunction of zero everywhere except
between x=0 and x=a, where it has a constant value of A. Determine the value of Ausing
the normalization condition.
9.30 Consider a one-dimensional problem that yields a wavefunction of zero everywhere except
between x=0 and x=a, where it has a value of Ax. Determine the value of Ausing the
normalization condition.
9.31 In a quantum-mechanical world, a baseball game is being played. A batter hits the ball
and an outfielder runs to catch the ball. He gets to the spot where the ball will land and
opens his glove. What is the probability that he will catch the ball? Assume the ball is
moving at a speed of 200 ±50 nm s−^1 , that it weighs 1.054 × 10 −^22 kg, and that the glove
has a diameter of 5μm.
9.32 In this quantum-mechanical world, a person who has a mass of 6.6 × 10 −^18 kg is running
through a tiny door that is only 100 nm wide. How fast does the person need to run such
that quantum effects become an important influence in determining where he ends up after
running through the door?
9.33Explain what unusual effects would occur if an electron was present in a three-dimensional
box that had very small sides of less than 0.1 Å.
singke
(singke)
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