# Questions tagged [schroedinger-equation]

Partial differential equation which describes the time evolution of the wavefunction of a quantum system. It is one of the first and most fundamental equations of quantum mechanics.

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### Do the symmetrized solutions to the time-independent Schrodinger equation span the symmetric functions?

Im learning QM from a book and after reading about multiparticle systems (for instance two noninteracting particles), it looks like the author found the solutions to the time-independent Schrodinger ...
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### Why is an eigenfunction $\psi_{n,l}$ proportional to $r^{l}$ close to the nucleus?

This is in reference to Quantum Physics of Atoms, Molecules, Solids, Nuclei and Particles by Robert Eisberg and Robert Resnick. The author writes Inspection of the eigenfunctions listed in table 7 - ...
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### What is the probability of measurement in QM, dependent on time?

Consider a QM system with an observable $A$ and orthonormal eigenbasis $\{|n\rangle,n=0,1,2,\ldots\}$. Then we know that if the system is in some state $|\psi\rangle$ and we measure $A$, the ...
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### Minimum energy eigenvalue [duplicate]

Why is the energy eigenvalue is always greater than minimum potential for a particle moving in a certain potential?
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### Fundamental state and its energy given a potential $V(x)$ [closed]

I have to answer same questions about this potential: $$V(x)= \begin{cases} 0 & x\in[0,2a]\\-\lambda\delta(x-a) \\+\infty & otherwise \end{cases}$$ Are there proper eigenfunctions and proper ...
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### Asymmetric potential well and discrete energy levels

Let us consider an asymmetric potential, which is piecewise defined as $V_1$ for $x<0$, $0$ when $0<x<a$ and $V_2$ for $x>a$, together with the condition $V_1 > V_2 >0$. In the first ...
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### Why is it selectively OK to rely on intuitive analogues when solving problems in Quantum Mechanics, such as the step potential problem?

I was looking at solved example (3.13) in the Schaum's Series book on QM by Yoav Peleg et al (2nd edn), where they solve for a step potential where a high energy particle is coming from the left and ...
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### Doubt in the completeness of wave function

I am reading about the completeness property of wave function. The following is given about it- The energy eigenstates are complete in the sense that any reasonable wave function $\psi(x)$ can be ...
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### Predicting the probability distribution in a potential

I've been dealing with a kind of problem in quantum mechanics, where they give us an arbitrary potential, and then ask us to predict the form of the probability amplitude or the wave function. The ...
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As I tried to learn quantum mechanics I have found two solutions of one-dimensional time-independent schrodinger equation in various resources. One is,$$\psi(x) = Asin(kx)+Bcos(kx)\\\text{where}, k = \... 1answer 44 views ### How to reconcile two different derivations of the time-independent Schrödinger equation? On one hand, using the Spectral decomposition of the Hamiltonian operator H, assumed to be an Hermitian operator, it is relatively simple to derive the equation U(t) = \sum |v_j\rangle\langle v_j| ... 0answers 35 views ### Schroedinger cat states of the harmonic oscillator I've found in an article that it is possible to prepare experimentally the superposition of two coherent (quasi-classical) states to obtain the Schroedinger cat state:$$ \left|\psi_{\pm}(t)\right\...
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I was thinking the other day, if you had the Schrodinger equation in 3-dimensions, and had a spherically symmetrical potential. Ie.: $$-\frac{ℏ^{2}}{2m}∇^{2}ψ+V(r)ψ=Eψ$$ Then you could simplify the ...
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### How can Bound state energy be negative if the $V_{min}$ is positive?

We know that Energy must be negative for bound states (as the wavefunction must go to 0 at infinity) but when we are looking at potential wells, we also say that E must be greater than the minimum ...
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### Born Rule proof for freshmen

Although early quantum mechanics are taught in many freshman courses, the Born Rule is almost never proved at that stage. Is it even impossible to elementarily prove that the probability density is ...
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### Solving the Schroedinger equation with the initial condition as an energy eigenstate [closed]

I was studying quantum mechanics by watching a video lecture series. In the lecture https://youtu.be/TWpyhsPAK14?list=PLUl4u3cNGP61-9PEhRognw5vryrSEVLPr&t=2784 , the professor tries to solve the ...
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### Why is the reflection coefficient 1 for step potentials where energy is less than the potential?

Consider a potential $V(x)$ which is zero when $x<0$ and $V_0>0$ when $x>0$. Suppose there is an incident particle with momentum $p=\hbar k$ and energy $E = \hbar^2 k^2 / 2m < V_0$ coming ...
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### In quantum mechanics when we use the real wavefunctions to find the average value of momentum operator then it comes out be zero. What does it mean? [closed]

In quantum mechanics when we use the real wavefunctions to find the average value of momentum operator then it comes out be zero. What does it signifies? Please explain it.
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### Scattering from finite square well and the transmission coefficient

Suppose we have a typical finite square well where $\lim_{x \to \pm\infty} V(x)=0$ and $V(x)=-V_0$ for all $x\in[-a,a]$ where $V_0>0$. The finite square well admits both bounds state solutions (...
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### For the even wavefunction and odd wavefunction, can we estimate whether the energy of the system is positive or negative?

For the even wavefunction and odd wavefunction, can we estimate whether the energy of the system is positive or negative? And for which of (odd or even wavefunction) energy is higher? You can consider ...
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### Is there any practical potential for which first derivative of wavefunction is continuous? [duplicate]

As we know that first derivative of the wavefunction is discontinuous when the potential is infinity. Is there any practical potential for which first derivative of wavefunction is continuous?
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### $k$-dependence of the energy in solid state physics

In a crystal, the electrons are subject to a periodic potential due to the fact that the atoms form a periodic lattice. From this periodicity we can obtain the Bloch theorem, and get a general formula ...
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