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So I am trying to solve ex. 14.3 in Schwartz textbook "Quantum Field Theory and the Standard Model" and in the second requirement, he wanted me to show that the action of the conjugate momentum operator $\hat{\pi}$ on $\hat{\phi}$ eigenstate is equal to the the action of the variation of $\phi$ to the same eigenstate:

$$\hat{\pi}(x) |\phi\rangle = i\hbar \frac{\delta} { \delta \phi(x)} |\phi\rangle $$

and I am stuck in that requirement.

So I am trying to solve ex. 14.3 in Schwartz textbook "Quantum Field Theory and the Standard Model" and in the second requirement, he wanted me to show that the action of the conjugate momentum operator $\hat{\pi}$ on $\hat{\phi}$ eigenstate is equal to the the action of the variation of $\phi$ to the same eigenstate:

$$ \langle\phi|\hat{\pi}(x) = -i\hbar \frac{\delta} { \delta \phi(x)} \langle\phi| $$

and I am stuck in that requirement.

So I am trying to solve ex. 14.3 in Schwartz textbook "Quantum Field Theory and the Standard Model" and in the second requirement, he wanted me to show that the action of the conjugate momentum operator $\hat{\pi}$ on $\hat{\phi}$ eigenstate is equal to the the action of the variation of $\phi$ to the same eigenstate:

$$\hat{\pi}(x) |\phi> = i\hbar \frac{\delta} { \delta \phi(x)} |\phi> $$

and I am stuck in that requirement.

So I am trying to solve ex. 14.3 in Schwartz textbook "Quantum Field Theory and the Standard Model" and in the second requirement, he wanted me to show that the action of the conjugate momentum operator $\hat{\pi}$ on $\hat{\phi}$ eigenstate is equal to the the action of the variation of $\phi$ to the same eigenstate:

$$\hat{\pi}(x) |\phi\rangle = i\hbar \frac{\delta} { \delta \phi(x)} |\phi\rangle $$

and I am stuck in that requirement.

So I am trying to solve ex. 14.3 in Schwartz textbook "Quantum field theory and the standard momentum" and in the second requirement, he wanted me to show that the action of the conjugate momentum operator $\hat{\pi}$ on $\hat{\phi}$ eigenstate is equal to the the action of the variation of $\phi$ to the same eigenstate:

$$\hat{\pi}(x) |\phi> = i\hbar \frac{\delta} { \delta \phi(x)} |\phi> $$

and I am stuck in that requirement.

So I am trying to solve ex. 14.3 in Schwartz textbook "Quantum Field Theory and the Standard Model" and in the second requirement, he wanted me to show that the action of the conjugate momentum operator $\hat{\pi}$ on $\hat{\phi}$ eigenstate is equal to the the action of the variation of $\phi$ to the same eigenstate:

$$\hat{\pi}(x) |\phi> = i\hbar \frac{\delta} { \delta \phi(x)} |\phi> $$

and I am stuck in that requirement.