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Consider the equation of motion for the expectation value of an operator $A$ $$\frac{d\langle A\rangle}{dt} = \frac{1}{i\hbar}\langle [A,H]\rangle + \left \langle \frac{\partial A}{\partial t} \right \rangle \, .$$ I am confused with the second term, $\langle \partial A / \partial t \rangle$. Why does $\langle \partial A / \partial t \rangle$ vanish for observables?

if the observable $A$ does not depend explicitly on time, the term $\langle \frac{\partial A}{\partial t}\rangle$ will vanish

-- Zettili's Quantum Mechanics Book

What does it really mean when $A$ is $X$ or $P_x$ for example? If $$\hat P_x= -i\hbar\frac{\partial }{\partial x}$$ then $$ \left \langle \frac{\partial \hat P_x}{\partial t} \right \rangle = \left \langle -i\hbar\frac{\partial}{\partial t} \left( \frac{\partial }{\partial x} \right) \right \rangle = ? $$ Why does it vanish and what does it really mean?

[I am very confused with the concept of the expectation value of an operator. I have checked these:

• Is the expectation value the same as the expectation value of the operator?
• Meaning of time derivative of an operator
• Quantum Mechanics: Time dependence of an expectation value
• http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/expect.html

I am getting more confused! ]

Consider the equation of motion for the expectation value of an operator $A$ $$\frac{d\langle A\rangle}{dt} = \frac{1}{i\hbar}\langle [A,H]\rangle + \left \langle \frac{\partial A}{\partial t} \right \rangle \, .$$ I am confused with the second term, $\langle \partial A / \partial t \rangle$. Why does $\langle \partial A / \partial t \rangle$ vanish for observables?

if the observable $A$ does not depend explicitly on time, the term $\langle \frac{\partial A}{\partial t}\rangle$ will vanish

-- Zettili's Quantum Mechanics Book

What does it really mean when $A$ is $X$ or $P_x$ for example? If $$\hat P_x= -i\hbar\frac{\partial }{\partial x}$$ then $$ \left \langle \frac{\partial \hat P_x}{\partial t} \right \rangle = \left \langle -i\hbar\frac{\partial}{\partial t} \left( \frac{\partial }{\partial x} \right) \right \rangle = ? $$ Why does it vanish and what does it really mean?

[I am very confused with the concept of the expectation value of an operator. I have checked these:

• Is the expectation value the same as the expectation value of the operator?

• Meaning of time derivative of an operator

• Quantum Mechanics: Time dependence of an expectation value

• http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/expect.html

  
  I am getting more confused! ]

$$\frac{d\langle A\rangle}{dt} = \frac{1}{i\hbar}\langle [A,H]\rangle + \langle \frac{\partial A}{\partial t}\rangle$$ I am confused with the second term, $\langle \frac{\partial A}{\partial t}\rangle$. Why does $\langle \frac{\partial A}{\partial t}\rangle$ vanish for observables?

"if the observable $A$ does not depend explicitly on time, the term $\langle \frac{\partial A}{\partial t}\rangle$ will vanish"

-Zettili's Quantum Mechanics Book

What does it really mean when $A$ is $X$ or $P_x$ for example?

$\hat P_x= -i\hbar\frac{\partial }{\partial x}$

Then $\langle \frac{\partial \hat P_x}{\partial t}\rangle=\langle -i\hbar\frac{\partial}{\partial t}(\frac{\partial }{\partial x})\rangle=$?
  Why does it vanish and what does it really mean?  

[I am very confused with the concept of the expectation value of an operator. I have checked these:

• Is the expectation value the same as the expectation value of the operator?
• Meaning of time derivative of an operator
• Quantum Mechanics: Time dependence of an expectation value
• http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/expect.html

I am getting more confused! ]

Consider the equation of motion for the expectation value of an operator $A$ $$\frac{d\langle A\rangle}{dt} = \frac{1}{i\hbar}\langle [A,H]\rangle + \left \langle \frac{\partial A}{\partial t} \right \rangle \, .$$ I am confused with the second term, $\langle \partial A / \partial t \rangle$. Why does $\langle \partial A / \partial t \rangle$ vanish for observables?

if the observable $A$ does not depend explicitly on time, the term $\langle \frac{\partial A}{\partial t}\rangle$ will vanish

-- Zettili's Quantum Mechanics Book

What does it really mean when $A$ is $X$ or $P_x$ for example? If $$\hat P_x= -i\hbar\frac{\partial }{\partial x}$$ then $$ \left \langle \frac{\partial \hat P_x}{\partial t} \right \rangle = \left \langle -i\hbar\frac{\partial}{\partial t} \left( \frac{\partial }{\partial x} \right) \right \rangle = ? $$ Why does it vanish and what does it really mean?

[I am very confused with the concept of the expectation value of an operator. I have checked these:

• Is the expectation value the same as the expectation value of the operator?
• Meaning of time derivative of an operator
• Quantum Mechanics: Time dependence of an expectation value
• http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/expect.html

I am getting more confused! ]

$$\frac{d\langle A\rangle}{dt} = \frac{1}{i\hbar}\langle [A,H]\rangle + \langle \frac{\partial A}{\partial t}\rangle$$ I am confused with the second term, $\langle \frac{\partial A}{\partial t}\rangle$. Why does $\langle \frac{\partial A}{\partial t}\rangle$ vanish for observables? "if the observable $A$ does not depend explicitly on time, the term $\langle \frac{\partial A}{\partial t}\rangle$ will vanish"

-Zettili's Quantum Mechanics Book

What does it really mean when $A$ is $X$ or $P_x$ for example?

$\hat P_x= -i\hbar\frac{\partial }{\partial x}$

Then $\langle \frac{\partial \hat P_x}{\partial t}\rangle=\langle -i\hbar\frac{\partial}{\partial t}(\frac{\partial }{\partial x})\rangle=$?
Why does it vanish and what does it really mean?

[I am very confused with the concept of the expectation value of an operator. I have checked these:

• Is the expectation value the same as the expectation value of the operator?
• Meaning of time derivative of an operator
• Quantum Mechanics: Time dependence of an expectation value
• http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/expect.html

I am getting more confused! ]

$$\frac{d\langle A\rangle}{dt} = \frac{1}{i\hbar}\langle [A,H]\rangle + \langle \frac{\partial A}{\partial t}\rangle$$ I am confused with the second term, $\langle \frac{\partial A}{\partial t}\rangle$. Why does $\langle \frac{\partial A}{\partial t}\rangle$ vanish for observables?

"if the observable $A$ does not depend explicitly on time, the term $\langle \frac{\partial A}{\partial t}\rangle$ will vanish"

-Zettili's Quantum Mechanics Book

What does it really mean when $A$ is $X$ or $P_x$ for example?

$\hat P_x= -i\hbar\frac{\partial }{\partial x}$

Then $\langle \frac{\partial \hat P_x}{\partial t}\rangle=\langle -i\hbar\frac{\partial}{\partial t}(\frac{\partial }{\partial x})\rangle=$?
Why does it vanish and what does it really mean?

[I am very confused with the concept of the expectation value of an operator. I have checked these:

• Is the expectation value the same as the expectation value of the operator?
• Meaning of time derivative of an operator
• Quantum Mechanics: Time dependence of an expectation value
• http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/expect.html

I am getting more confused! ]