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.

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Why don't we have particles whose wavefunctions are symmetric wrt one exchange operator and anti-symmetric wrt other exchange operator?

Consider a system with $n$ identical particles. Let the wavefunction of the system be $\psi(r_1,\ldots, r_2)$. Let $P_{a,b}$ represent the exchange operator which exchanges particle $a$ with particle ...
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1answer
142 views

Boundary Conditions in a Step Potential

I'm trying to solve problem 2.35 in Griffith's Introduction to Quantum Mechanics (2nd edition), but it left me rather confused, so I hope you can help me to understand this a little bit better. The ...
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5answers
303 views

How do we know that electron wave function extends to infinity?

Why do physicists assume this? Is it a proven fact that wave function extends to infinity or just a theory? Would it make sense if they didn't extend to infinity?
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1answer
236 views

Are wave functions real physical objects? [duplicate]

Are wave functions (ex. electron waves) real physical objects or just mathematical tools?. Some researchers say that they have proof that they are real objects. Here's [the link] ...
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1answer
72 views

What is the implication that the Schrodinger equation be solved by both real and imaginary part of the wave function? [closed]

Suppose $\psi = \psi_{real} + i \psi_{imag}$ be the wave function, then both $\psi_{real}$ and $\psi_{imag}$ can be used to solve the Schrodinger's equation This can be demonstrated by plugging ...
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1answer
103 views

How to minimize the wavepacket dispersion?

This is a final exam problem. Here is what I can remember: We know that if an electron's wavefunction starts out as a narrow wavepacket, and moving in a region of constant potential, then the ...
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0answers
49 views

wavefunction and contextuality

According to the French philosopher Michel Bitbol, the "deep-lying connection between the contextual character of observables, and the wave-like form of probability distributions was demonstrated ...
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1answer
154 views

What is the energy of a Gaussian wave packet?

Suppose we have a potential barrier situation, that is $V(x)$ is zero everywhere except on the interval $[-a,a]$, where it is equal to some $V_0 > 0$. Introduce some Gaussian shaped wave packet to ...
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1answer
120 views

Should the differential of a wavefunction have a time partial derivative?

In chapter 1 of Griffths' QM text, he shows that $\frac{\mathrm{d}}{\mathrm{d}t}\int_{-\infty}^{\infty}|\Psi|^2\,\mathrm{d}x=0$ by noting $$\begin{align} ...
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2answers
367 views

Wave function in quantum mechanics

I was wondering about something while studying quantum mechanics. If the wave function collapses when measuring a particle and assumes a single position, how do we know that it was a wave in the first ...
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1answer
38 views

The wave function of transverse one is different from longitude one for convenience?

I use the book Fundamental of Physics Hallidays&Resnick 10th Edition Jearl Walker to study in my physics class while I got myself University Physics with Modern Physics Sears, Zemansky 13th ...
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1answer
87 views

Why two-particle wavefunctions are separable and their corresponding particles are indistiguishable at the same time?

If the wavefunction $\psi(r_1,r_2)$ doesn't represents an entangled state, it is separable: $$\psi(r_1,r_2)=\psi_a(r_1)\psi_b(r_2)$$ In this treatment, we ignore the interaction between two particles ...
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1answer
197 views

photon polarization, uncertainty in Energy

A beam of red light is sent along the $z$ axis through a polaroid filter that passes only $x$ polarized light. The beam is initially polarized at $30$°, and the total energy is $10$ Joules. Estimate ...
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1answer
276 views

Energy difference between symmetric and antisymmetric wavefunctions [closed]

Is there any energy difference between a particle in a symmetric wavefunction and an identical particle in an identical potential but in a state with an anti-symmetric wavefunction? Or is it ...
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0answers
20 views

Oscillators with anharmonic interaction terms

I'm looking for papers modeling oscillators coupled with anharmonic interaction terms. The term is combination of a linear element and a Gaussian kernel that decays proportionally to the difference of ...
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1answer
82 views

Effect of pressure increase on electron orbital wave functions

One of my nuclear physics exercises was to find out if increasing the pressure of a sample of $^{7}\textrm{Be}$ would increase the chance of electron capture to $^{7}\textrm{Li}$ occur. My reasoning ...
2
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2answers
55 views

Does an excited state wave function depend on state preparation?

Consider a quantum system with a ground state and many excited states (e.g. an atom). If the system is in an excited state, to what extent does its wave function depend on the method of state ...
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5answers
355 views

How does a Wavefunction collapse?

I have been wondering and researching... How does a wavefunction collapse into one state?More specifically, what conditions cause a wavefunction for a quantum particle to collapse? Does this have to ...
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3answers
780 views

Superconducting Wavefunction Phase (Feynman Lectures)

In Volume 3, Section 21-5 of the Feynman lectures (superconductivity), Feynman makes a step that I can't quite follow. To start, he writes the wavefunction of the ground state in the following form ...
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0answers
39 views

Wavefunction renormalisation in first order perturbation theory

I just read the following in the context of scattering amplitudes in QFT: Note that the wavefunction renormalisation factor $Z$ itself is of the form $1 + \mathcal{O}(\lambda)$ in perturbation ...
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1answer
69 views

Allowed energies for semi-harmonic oscillator

Question: If a particle is attached to a semi-harmonic oscillator (that is, for example, the spring is stretchable but not compressible) such that the potential $V(x)$ is infinity for $x\leq0$ and ...
3
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2answers
86 views

Is $\phi_n =\left\langle \vec r | n \right\rangle $ the photon wave function?

I am a bit confused about this issue and I am still not clear whether is there is a photon wave function or not. Since we use Fock states $| n \rangle$ to represent the state of a quantized ...
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3answers
81 views

Does there exist a hyperbolic relationship between frequency $\omega$ and wavenumber $k$?

As the title states, is it possible to derive a hyperbolic relationship in the form of $\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1$ between frequency $\omega$ and wavenumber $k$ I have tried to start this ...
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2answers
359 views

Hilbert space and Hamiltonians

Assume a system described by a Hamiltonian H, and assume that the eigenstates of H, $φ_i$(r) are integrable in absolute square. We say that these states belong to a Hilbert space (they can even form a ...
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1answer
284 views

Interpretation of Dirac equation states

In Pauli theory the components of two-component wavefunction were interpreted as probability amplitudes of finding the particle in particular spin state. This seems easy to understand. But when ...
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2answers
687 views

Normalization of Momentum Eigenfunctions: the number of particles

After finding the eigenfunctions $u_p(x)=Ce^{ipx/\hbar}$ of the momentum operator just like in this UCSD lecture notes, one seeks to normalize them, so one first tries: ...
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1answer
81 views

Quantum Wavefunctions Without Space

A handful of physicists have a rather peculiar definition of 'nothing' in terms of cosmology. Their claim is that the Universe, assuming it has 0 total energy, could have arisen from nothing but ...
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Estimate of the second shallowest bound state?

Suppose we have a 1D potential $V(x)$ of finite range, i.e., $$ V(x) ~=~0 $$ for $|x| > b $. The potential is assume to support at least two bound states, but might have more, say $n\geq 2$. ...
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11answers
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About the complex nature of the wave function?

1. Why is the wave function complex? I've collected some layman explanations but they are incomplete and unsatisfactory. However in the book by Merzbacher in the initial few pages he provides an ...
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2answers
1k views

How to know if a wave function is physically acceptable solution of a Schrödinger equation?

How does one decide whether a wave function is a physically acceptable solution of the Schrödinger equation? For example: $\tan x$ , $\sin x$, $1/x$, and so on.
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2answers
540 views

Bloch wave function orthonormality?

there is this text book that is giving me a hard time for a while now: It shows that Bloch wave functions can be written as $$\Psi_{n\vec{k}}\left(\vec{r}\right) = \frac{1}{\sqrt{V}}e^{i\vec k \vec ...
3
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1answer
235 views

1D Finite potential well: solutions with $\sinh$ and $\cosh$?

So I am studying the (one dimensional) quantum mechanical finite potential well defined by: $$ V(x) = \cases{0, &|x|>a\cr -V_0, &|x|<a} $$ where $V_0>0$ is a real number. I know ...
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0answers
2k views

Solution for the Finite 2D Potential Well - Rotational Symmetry [closed]

I was searching for the eigensolutions of the two-dimensional Schrödinger equation $$\mathrm{i}\hbar \partial_t \mid \psi \rangle = \frac{\mathbf{p}^2}{2m_e}\mid \psi \rangle + V \mid \psi ...
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4answers
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Confused over complex representation of the wave

My quantum mechanics textbook says that the following is a representation of a wave traveling in the +$x$ direction:$$\Psi(x,t)=Ae^{i\left(kx-\omega t\right)}\tag1$$ I'm having trouble visualizing ...
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1answer
135 views

Bohr-Sommerfeld quantization for different potentials

Let's have Bohr-Sommerfeld quantization for one-dimensional case: $$ \int \limits_{a}^{b} p(x)dx ~=~ \pi \hbar (n + \nu ). $$ Here $p(x) = \sqrt{2m(E - U)}$, $a, b$ are turning points, and the area ...
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3answers
164 views

A misunderstanding regarding infinite square well

Here is a picture of the energy states of infinite potential well. We can see That the first level have a half wavelength which fittes with a full wave of the second level. $$\frac{ \lambda _{1} ...
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3answers
116 views

Question about derivation of the Heisenberg Uncertainty Principle?

I am looking at the derivation presented here. The first thing I am unsure about is where the form of $\psi_0=Ae^{\frac{-m\omega x^2}{2\hbar}}$ came from. Also, is this form for all $\psi$, or just ...
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1answer
736 views

Bohr-Sommerfeld quantization from the WKB approximation

How can one prove the Bohr-Sommerfeld quantization formula $$ \oint p~dq ~=~2\pi n \hbar $$ from the WKB ansatz solution $$\Psi(x)~=~e^{iS(x)/ \hbar}$$ for the Schroedinger equation? With $S$ the ...
5
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2answers
287 views

Ground state of Spherical symmetric potential always have $\ell=0$?

I was given a problem where I have a spherically symmetric potential (the exact form is not relevant to this question, I think - but anyway is it 0 for $r\in[a,b]$ and $\infty$ everywhere else) and I ...
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2answers
146 views

Why is time evolution of wavefunctions non-trivial?

(Note: This post focuses on a single simple example, however I'm asking about the error in general in my logic). Consider the infinite potential well "particle in a box" system described by ...
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4answers
787 views

Complex Conjugate of Wave Function

I've been reading through Griffiths QM book, and the only thing bugging me is they never fully described what $\Psi^* $ should be for any given function. I know it's the complex conjugate at the same ...
0
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4answers
56 views

Question about interpreting probabilities in QM [duplicate]

For the example of an infinite square well, $\psi(x)=0$ for $x$ outside the well/interval, and we are to interpret this as the particle cannot be found outside the well because ...
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3answers
734 views

Is there only radial motion in the Hydrogen ground state?

The ground state of the Hydrogen atom is spherically symmetric. In other words, the wave function Psi depends only on the distance r of the electron from the nucleus. As a consequence all ...
3
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3answers
567 views

Wavefunction, probability and impossible events

A friend of mine asked me a question, which I considered trivial at first, but after a while gave rise to some doubts. For instance, we have a potential well in 1 dimension defined by $$ V(x)= ...
3
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4answers
835 views

Is the wave function of a particle re-created after a measurement stops?

Yeah, I haven't quite understood, or been told, what happens to, for example an electron and it's wavefunction, when you stop to measure it? I mean, an electron has a wave function describing it's ...
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0answers
31 views

Why isn't there a different phase after fourier transformation in two lattices

I am trying to understand some solutions for graphenes energy dispersion. While most of it is clear, I don't get one step, when changing into k-space. Consindering two sublattices A and B with ...
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4answers
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Why the statement “there exist at least one bound state for negative potential” doesn't hold for 3D case?

Previously I thought this is a universal theorem, for one can prove it in the one dimensional case using variational principal. However, today I'm doing a homework considering a potential like ...
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2answers
630 views

Linear vs. quadratic dispersion relation

In wave mechanics the dispersion relation between frequency $\omega$ and wave number $k$ is linear: $$\omega_n=c k_n$$ But in quantum mechanics, based on Schrödinger's equation, one can show that we ...
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1answer
69 views

Do quantum physics apply universally at all scales? [duplicate]

Do quantum physics apply universally at all scales? Where do quantum physics apply? Does the nucleus of an atom abide by the laws of quantum physics? Like do we know the definitive/velocity ...
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2answers
95 views

How would you go about evaluating $\langle \psi \mid 100 \mid \psi \rangle$? [closed]

How would you go about evaluating $\langle \psi \mid 100 \mid \psi \rangle$? I just can't seem to figure this out, and I know it isn't hard.