# Questions tagged [integration]

For questions about problems related to physics that involve evaluating integrals. Purely mathematical questions should be asked at math.SE.

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### $\int_{-\infty}^{\infty} |\psi(x)|^2 ~ dx = 1$ when $\psi(x) = C\exp\left(\frac{x^2}{2a^2} + \frac{ix^3}{3a^3}\right)$

The information given is: Consider a state $|\psi\rangle$ describing a quantum particle on a line, whose position representation $\langle x|\psi\rangle = \psi(x)$ is given by: \begin{gather*} \...
0answers
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### Evaluation of Gaussian integral $\int^\infty_{-\infty}dx\;\exp(A(x-B)^2)$ with $A$, $B$ complex [migrated]

Does $$I = \int^\infty_{-\infty}dx \;\exp(re^{i\theta}(x-B)^2), \quad B \in \mathbb{C}$$ have a known standard result? I am hoping to use the result for exercises in the path integral formulation of ...
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### Operator integral [closed]

Consider the following integral: \begin{equation} L =2 \int_{0}^{\infty} d t \exp\left\{-\hat{\rho}_{\lambda} t\right\} \partial_{\lambda} \hat{\rho}_{\lambda} \exp\left\{-\hat{\rho}_{\lambda} t\right\...
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### Infinite dimensional generalization of the fundamental theorem of calculus

Can we generalize the fundamental theorem of calculus $$\frac{d}{dx} \int_0^x f(t) dt = f(x)$$ to path integrals $$\frac{d}{dx} \int_{q(0)=0}^{q(1)=x} \mathcal F[q] \, D q = \, ?$$
0answers
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### Understanding Variational Integrators for simulating Lagrangian mechanics

so I'm mostly a self-taught physicist, hence my general knowledge/understanding is a bit lacking. I'm trying to understand a bit better, on the intuitive level especially as well on the algorithmic, ...
1answer
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### Why do I get different results in the draining tank problem?

This is a sketch of the situationWe have to do a small mathematical paper for our school in which we wanted to describe the water that flows out of the cylinder with a differential equation. We also ...
2answers
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### Finding the centre of mass in polar coords with double integrals

The centre of mass of a body can be found using the general formula: $$\bar{\boldsymbol{r}} = \frac{1}{M} \int \boldsymbol{r} \ \mathrm{d}M$$ (RHB, p. 195)*. When I try to use this method with polar ...
1answer
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### Euler-Maclaurin-Formula and Finite Size Scaling

I am reading the book "Quantum Inverse Scattering Methode". In this book and in many other papers one looks at finite-size scaling. In this methode one uses often the Euler-MacLaurin-...
0answers
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### Integration by parts of covariant derivatives in QED

I am reading Sidney Coleman's QFT ch. 27 (in particular Eq. (27.73)) where he said that we can use integration by parts to write the term in the action \begin{equation} \int d^4x (\mathcal{D}^{\mu} \...
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### Aharanov-Bohm Effect Gradient of Line Integral

In Griffiths' Quantum Mechanics 2nd edition section 10.2.3 the phase $$g(\mathbf{r}) = \frac{q}{\hbar}\int_{O}^{\mathbf{r}}\mathbf{A}(\mathbf{r}')\cdot d\mathbf{r}'$$ is defined. It is noted that this ...