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A wave function in quantum physics is a mathematical description of the quantum state of an isolated quantum system in position or momentum space. The wave function is a complex-valued probability amplitude, and the probabilities for the possible results of measurements performed on the system can be derived from it. The most common symbols used to denote the wave function, are the Greek letters \(\psi \) or \(\Psi \) (lowercase and uppercase psi, respectively).
Eigenvalues and vectors: a.u.
In quantum mechanics, perturbation theory is a set of approximation schemes related to mathematical perturbation describing a complex quantum system in terms of a simpler one. The idea is to start with a simple system for which a mathematical solution is known, and add an additional “perturbing” Hamiltonian representing a weak perturbation for the system. If the perturbation is not too large, various physical quantities associated with the perturbed system (for example, its energy levels and eigenstates) can be expressed as “corrections” to those of a simple system. These corrections, being small in comparison with the size of the quantities themselves, can be calculated using approximate methods, such as asymptotic series. Thus, a complex system can be studied based on simpler one.
Please enter the perturbation method:
\(\delta V = qFx\):
Enter the perturbation criteria:
\(\delta V = qFx\sin(\omega_p t)\):
\(\delta V = \frac{\epsilon \eta}{2\sigma_x \sqrt{\pi}} e^{-\left(\frac{x-x_c}{\sigma_x}\right)^2} \):
Enter the perturbation criteria:
\(\delta V = -m_z \mu_B B \):
Enter the perturbation criteria:
\(q=\) , \(F=\)
Enter frequency for perturbation theory:
\(\omega_p=\)
Enter the number of frequencies for sinusoidal perturbation scan:
\(N_{\omega_p}=\)
Please enter the minimum / maximum frequency for scan perturbation: \(\omega_p^{min}=\), \(\omega_p^{max}=\)
select the frequency for the visualisation of the perturbation potential:
\(x_c=\) , \(y_c=\) , \(\sigma_x=\) , \(\sigma_y=\) , \(\eta=\) , \(\epsilon=\) \(m_z=\) , \(B=\) Enter function for perturbation profile
\(dV(x)=\)
Show probability
probability spectra
In this section, wave propagation (the initial state of which is given by the Gaussian profile in the previous section) through the barrier is simulated. In other words, here we can analyze the temporal evolution of the wave packet in the barrier system.
In quantum mechanics, the expected value is the probabilistic expected value of the result (measurement) of an experiment. It can be considered as an average of all possible measurement results, weighted by their probability.
Consider an operator \( \hat{A} \). The expectation value is then \( \langle A \rangle = \langle \psi |\hat{A}| \psi \rangle \) in Dirac notation with \( | \psi \rangle \) a normalized state vector.
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