# Questions tagged [wavefunction]

A complex scalar field that describes a quantum mechanical system. The square of the modulus of the wave function gives the probability of the system to be found in a particular state. DO NOT USE THIS TAG for classical waves.

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### Relativistic Velocity [closed]

As a particle has enough relativistic velocity, it’s mass should have a noticeable increase. How does this translate into the particle’s wave function? Is there a difference between an elementary ...
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### Probability current calculations

I have a question about the probability current density. Because I cant really understand the meaning of that (how can we relate something real like a current to something abstract such as probability)...
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### Are particles literally waves or just abstract probability waves?

In introductory quantum physics, particles are described by the Schrodinger equation wave-function, which describes only an abstract probability wave. But in quantum field theory, particles are ...
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### Symmetric infinite well potential

Assume we have the following potential : $$V\left(x\right)=\begin{cases} 0 & -\frac{L}{2}\leq x\leq\frac{L}{2}\\ \infty & else \end{cases}$$ The wave function for a particle in this well ...
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### Bound states and scattering states - Time-dependent Schrödinger equation

If we have a quantum system described by the time-independent Schrödinger equation (TISE): \begin{equation} -\frac{\hbar^{2}}{2 m} \frac{d^{2} \psi}{d x^{2}}=E \psi \end{equation} We have two possible ...
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### Relation between Matrix mechanics and Wave mechanics [closed]

What is the relationship between Hamiltonian operator (matrix), position operator (matrix) and momentum operator (matrix) in Matrix mechanics and wave mechanics?
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### Proof bound states exist on vanishing, negative potentials in 1D

I want to prove the following: Show that for any one dimensional, time independent potential $U(x)$, where $\lim\limits_{x \rightarrow \infty}{U(x)} = 0$ and $\int_{-\infty}^{\infty}U(x) < 0$ ...
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### One-body operator for fermions - equality

I am reading Modern Many-Particle Physics by Lipparini. In chapter 1.5 he talks about the matrix elements of the one-body operator: $$F_1 = \sum_{i=1}^{N}f(x_i)$$ He mentions that the matrix elements ...
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### Can we make a symmetric wavefunction out of two anti-symmetric wavefunctions?

And, if so, then can be say that we've made a boson out of two fermions? Mathematically, If f=fermion=f(x,y) then b=boson=[f(x,y)-f(y,x)]/2
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### What happens to a function generator waveform when another capacitor is added in parallel with an existing capacitor in a circuit?

I am trying to gain an understanding of the first-order response of RC circuits and measurement of capacitance in a capacitive sensor using function generation and oscilloscopes. I had a question ...
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### Proper way of adding parameters to a test wave function

So experimenting with the variational method, I thought of a test wave function for an infinite deep well system, $$\Psi(x) = N(a^2-x^2) \text{ for -a < x < a}$$ and $0$ everywhere else. ...
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### Eigen-energy in Finite Quantum Well

So I'm a beginner at quantum mechanics and I'm learning about finite quantum wells. I've been stuck on an example on how to find Eigen-energies in conduction and valence bands of the quantum well ...
Why is there a behaviour where $E_1$ and $E_2$ are close to each other? This question is already answered before but I did not understand the explanation about symmetric and asymmetric terms as I do ...
Suppose we have some ion such as $H_2^+$ and we produce some trial electronic wavefunction. For example, we take the simple trial wavefunction made up of a single 1s orbital of the hydrogen atom ...