Circular-wave dualism

Содержание и основные понятия

Quantum objects show particle properties in registration and wave patterns in probability distribution. De Broil connected the particle's pulse with the wave length.
GEF · 11 grade
PIF · Baseline
Interactive model
dualism
Wave de Broil
Probability
uncertainty
01
The physical picture
What happens and what boundaries the model has.
Main message
Quantum objects show particle properties in registration and wave patterns in probability distribution. De Broil connected the particle's pulse with the wave length.
Electronics give a diffuse picture.
Measurement changes the available information about the system.
The principle of uncertainty limits the joint accuracy of the coordinate and pulse.
How to reason
First, name the system and the interaction, then select the values, and only then write down the law. The formula works within the model's assumptions.
02
Laws and values
Symbols should be read as a relationship of values, not as a recipe for substitution.
λ
=
h
p
\lambda=\frac{h}{p}
λ
=
p
h
​
Wave de Broil
Δ
x
Δ
p
≥
ℏ
2
\Delta x\,\Delta p\ge\frac{\hbar}{2}
Δ
x
Δ
p
≥
2
ℏ
​
uncertainty
Review of the situation
The more accurate the electrons are, the wider the inevitable range of possible impulses.
04
Links and application
In the real world
The more accurate the electrons are, the wider the inevitable range of possible impulses.
Model verification
Compare the prediction with observation, evaluate the units, the order of magnitude and the influence of the factors not taken into account. Disparity does not always mean an error of law: often idealization is no longer sufficient.
C
What needs to be understood
Outcome 1
Explain the physical meaning of the topic "Coral-wave dualism" through the model, not just the formula.
Outcome 2
Distinguish and correctly use terms: dualism, wave de Broil, probability.
Outcome 3
Indicate the conditions for the applicability of the law, verify units and limit cases.
T
Terms of the topic
The definition should indicate the physical meaning, not a substitute for a domestic synonym.
dualism
Quantum principle, that objects display the corral and wave properties of different experiments.
Wave de Broil
Quantum mechanical wave compared to the particle with the pulse p and length h/p.
Probability
The numerical measure of the possibility of an accidental event; the quantum theory is determined by the state of the system.
uncertainty
The characteristic variation of the possible results of the quantum measurement in the specified state.
F
Origin and conclusion of the formulas
The fundamental law cannot be "proven" by algebras: for each record, it is stated whether it is a definition, an experimental law, or a model effect.
λ
=
h
p
\lambda=\frac{h}{p}
λ
=
p
h
​
Postulate or Model
A wave of broiling.
The following is an indication of the definition, experience or law from which this entry arises and where it is applicable.
p
γ
=
h
λ
p_\gamma=\frac{h}{\lambda}
p
γ
​
=
λ
h
​
For a photon, wave length is already connected to impulse.
λ
=
h
p
\lambda=\frac{h}{p}
λ
=
p
h
​
De Broil postulated the same bond for any free material particle.
p
=
m
v
⇒
λ
=
h
m
v
p=mv\quad\Rightarrow\quad\lambda=\frac{h}{mv}
p
=
m
v
⇒
λ
=
m
v
h
​
In the non-relativist limit, the pulse can be replaced by a product of mass and speed; the diffusion of electrons confirms the prediction.
Conditions:
A free particle with a given pulse p; a relativist pulse should be used for the relativity particle, not mv.
Monitoring:
The dimensions of both parts shall coincide; the result shall be checked for sign, order and limit case.
Δ
x
Δ
p
≥
ℏ
2
\Delta x\,\Delta p\ge\frac{\hbar}{2}
Δ
x
Δ
p
≥
2
ℏ
​
model effect
Uncertainty.
The following is an indication of the definition, experience or law from which this entry arises and where it is applicable.
ψ
(
x
)
=
∫
ϕ
(
k
)
e
i
k
x
d
k
\psi(x)=\int\phi(k)e^{ikx}\,dk
ψ
(
x
)
=
∫
ϕ
(
k
)
e
ik
x
d
k
Localized quantum state is built as a superposition of waves with different wave numbers k.
Δ
x
Δ
k
≥
1
2
\Delta x\,\Delta k\ge\frac12
Δ
x
Δ
k
≥
2
1
​
For the function and its furie spectra, mathematical inequality limits the simultaneous narrowness of distribution.
p
=
ℏ
k
⇒
Δ
x
Δ
p
≥
ℏ
2
p=\hbar k\quad\Rightarrow\quad\Delta x\,\Delta p\ge\frac{\hbar}{2}
p
=
ℏ
k
⇒
Δ
x
Δ
p
≥
2
ℏ
​
The quantum connection of the pulse to the wave number turns this restriction into a ratio of uncertainty.
Conditions:
Δx and Δp are standard deviations from co-ordinate measurements and the corresponding pulse components in one quantum state.
Monitoring:
The dimensions of both parts shall coincide; the result shall be checked for sign, order and limit case.
!
Model boundaries and typical errors
Error: Forget model condition
You can't move the formula to any situation just because it's a coincidence of letters. The key condition of this topic is that electronics give a diffuse picture.
How to Check the Mind
Measurement changes the available information about the system. Then check the units, vector direction, and the behaviour of the result at zero or very large parameter.
School model boundary
The de Broyle wave is deep, and the principle of uncertainty is a qualitative element of the modern physical picture of the world. It does not describe the lack of precision of the instrument: restrictions are placed in the quantum state itself. The classic trajectory becomes a good approach when the characteristic operation of the system is much larger than the permanent Planck.
Σ
Conclusion on the topic
Circular-wave dualism
Quantum objects show particle properties in registration and wave patterns in probability distribution. De Broil connected the particle's pulse with the wave length.
Electronics give a diffuse picture.
Measurement changes the available information about the system.
Any numerical result shall be accompanied by a unit, a sign and an explanation of its physical meaning.
The content is consistent with the FRP on Physics of the OS/OSS 2025 and the subject matter of the current lines of the PNP: I. M. Peryškin and co-authors (7–9), G. J. Mäkishev and coauthors (10–11), and with the lines "Engineers of the Future" and V. A. Kasyanov. The original texts are not reproduced, the text of the textbooks is not reproduced.