All Questions
Tagged with wavefunction fourier-transform
164
questions
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How to Perform Fourier Transform on a Quantum State of Spin-1/2 Particle?
I am currently studying quantum mechanics and need help understanding how to perform the Fourier transform of a particular state. I have a spin-1/2 particle whose momentum and spin state at time $t=0$ ...
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2
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70
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Basic confusion about evolution of wave function of a free particle
I am going through Griffith's introduction to quantum mechanics. An example for a free particle is given where
$$\Psi(x,0) = \begin {cases}A \quad \text{if } x\in [-a,a]\\ 0\quad \text{otherwise}\end{...
- 1,772
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A simple question in quanum mechanics on position and momenum eigenstates
The eigenfunctions (eigenstates) for the momentum of a particle are given by the plane waves
$$\phi(x,t) = \sin(kx - \omega t)$$
If we sum a large number of these waves in a range from $0$ to $k_m$, ...
- 113
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Gaussian wave packet with complex coefficients [closed]
I am trying to obtain a representation of the momentum-space wavefunction $<p'|\alpha>$
Its position space wavefunction is given as
$$ <x'|\alpha> = N \exp [-(a+ib)x'^2 +(c+id)x'] $$
where ...
- 11
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87
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Is complex integration needed when normalizing a wave function?
I have to find $\phi_0$ from following wave function in the momentum space:
\begin{equation}
\phi(k) = \phi_0 \text{exp}\bigg(-\frac{(k-k_0)^2}{2\kappa^2}\bigg)
\end{equation}
I know that I have to ...
- 109
1
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1
answer
105
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Wave packet for particle in a potential
In the book Quantum Mechanics by Cohen-Tannoudji, the author explains that the solutions of the Schrodinger equation of a free particle in one dimension are plane waves:
$$\psi (x, t) = A e^{i(kx-\...
- 98
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109
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Relationship between position kets in different topologies
Consider a particle moving on a ring $\mathcal{S}^1 \sim \mathbb{R} / \mathbb{Z}$ of circumference $L$. Due to periodic boundary conditions,
$$
\langle x\mid p_n\rangle=\frac{1}{\sqrt{L}}e^{ip_{n}x/\...
- 31
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Discrete Schrödinger equation and Fourier transformation
I am currently working on an exercise involving the discretized version of Schrödinger's equation in an infinite potential well. The problem involves a well with a width of 1 and assumes $$\frac{\hbar}...
1
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2
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167
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Why can $ϕ(p)$ be Fourier expanded to $ψ(x)$ in quantum mechanics? [closed]
I know the Fourier transform is $$
F(\omega)=\int_{-\infty}^{\infty} f(x) e^{-i \omega x} \,d x
$$
$$
f(x)=\frac{1}{2 \pi} \int_{-\infty}^{\infty} F(\omega) e^{i \omega x} \,d \omega,
$$
but in ...
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Cohen Quantum Mechanics Derivation? [closed]
I dont understand the argument on page 38 eq. (C-6) of Cohen's quantum mechanics. Could someone break down for me what is $g(k)$? Is it the initial condition?
- 109
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1
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203
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Deriving the Heisenberg uncertainty principle from the wave packet [closed]
How did we get the C-17, is it possible to derive the Heisenberg uncertainty principle from the wave packet?
could you recommend readings to help me understand this better.
- 41
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0
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45
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Spatial spread of a relativistic particle [closed]
I am trying to figure out a picture of the wave properties of relativistic particle, e.g., particle produced at collider. It seems that the particle detected at collider have well defined momentum and ...
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2
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Why does superposing an infinite number of waves of different wavenumbers eliminate periodicity and may sometimes result in a localised wave?
I am studying how wave packets are defined in quantum mechanics, but I am finding it hard to intuitively understand why superposing an infinite number of waves of different wavenumbers $k$ may ...
- 390
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How is the space of $\mathcal{H}_{x}$ and $\mathcal{H}_{\xi}$ connected? [closed]
It might be a silly question, but I really don't know. There're 3 things I want to ask:
For example, with Schrödinger's equation $i\partial_{t}\psi = H\psi$ , where $\psi_{n}(x)$ are the ...
- 49
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How exactly do the coordinates of a vector in Hilbert space define a function?
I'm reading 'Teach Yourself Quantum Mechanics' by Alexandre Zagoskin.
In chapter 2 he introduces Hilbert spaces by starting with the fact that a function may be defined by its Fourier coefficients. ...
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