ObservableOperatorClassical counterpartPositionx = x:And so forth for coordinatesother than xMomentum (linear)Px = mvxPx = -ih-And so forth for coordinatesother than xMomentum (angular)Lx = yP: - zPyI, = - ih ŷazmi -K = =mv;Kinetic energy, 1-D%3DK =2m dx2mKinetic energy, 3-D+ v, + v)%3D+2m axdy az,pi + p; + p?2mPotential energy:Harmonic oscillatorkx².V = -kx%3DCoulombic91 9291 92V =%3D4TEorh? ( a?ayTotal energy+ V H=2mP + V2m axaz Is the function w(x) = sinx an eigenfunction for the linear momentumoperator, 6.? If yes, what is the eigenvalue?O Yes, the eigenvalue is -1Yes, the eigenvalue is sinxO Yes, the eigenvalue is – inO No

s the function w(x)= sinx an eigenfunction for the linear momentum pperator, 6,? ? If yes, what is the eigenvalue? O Yes, the eigenvalue is -1 O Yes, the eigenvalue is sinx Yes, the eigenvalue is – iħ No

s the function w(x)= sinx an eigenfunction for the linear momentum pperator, 6,? ? If yes, what is the eigenvalue? O Yes, the eigenvalue is -1 O Yes, the eigenvalue is sinx Yes, the eigenvalue is – iħ No

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 10.11E: Indicate which of these expressions yield an eigenvalue equation, and if so indicate the eigenvalue....

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Techniques and applications of quantum theory

Quantum theory, often known as quantum physics, is the foundation of modern physics and encompasses the nature and behavior of matter and energy at the atomic and molecular levels. As the exact nature and behavior of atomic and subatomic particles are impossible to determine, the laws of classical physics do not apply to this discipline. As a result, quantum field theory is primarily based on assumptions and probabilities.

Question

Observable
Operator
Classical counterpart
Position
x = x:
And so forth for coordinates
other than x
Momentum (linear)
Px = mvx
Px = -ih-
And so forth for coordinates
other than x
Momentum (angular)
Lx = yP: - zPy
I, = - ih ŷ
az
mi -
K = =mv;
Kinetic energy, 1-D
%3D
K =
2m dx
2m
Kinetic energy, 3-D
+ v, + v)
%3D
+
2m ax
dy az,
pi + p; + p?
2m
Potential energy:
Harmonic oscillator
kx².
V = -kx
%3D
Coulombic
91 92
91 92
V =
%3D
4TEor
h? ( a?
ay
Total energy
+ V H=
2m
P + V
2m ax
az

Is the function w(x) = sinx an eigenfunction for the linear momentum
operator, 6.? If yes, what is the eigenvalue?
O Yes, the eigenvalue is -1
Yes, the eigenvalue is sinx
O Yes, the eigenvalue is – in
O No

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