Quantum State Calculator

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✖Quantum Number is a numerical value that describes a particular aspect of the quantum state of a physical system.ⓘ Quantum Number [n]			+10% -10%
✖Mass of Particle is defined as the total mass of the considered particle.ⓘ Mass of Particle [M]			+10% -10%
✖Potential Well length is the distance from electron where potential well length is equal to infinite.ⓘ Potential Well Length [L]			+10% -10%

✖Energy in Quantum State refers to the total energy associated with a particular state of a quantum system. It represents the amount of energy that the system possesses in that specific state.ⓘ Quantum State [E_n]

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Formula

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Quantum State

Formula

`"E"_{"n"} = ("n"^2*pi^2*"[hP]"^2)/(2*"M"*"L"^2)`

Example

`"8.2E^-24eV"=(("2")^2*pi^2*"[hP]"^2)/(2*"1.34e-5kg"*("7e-10")^2)`

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Quantum State Solution

STEP 0: Pre-Calculation Summary

Formula Used

Energy in Quantum State = (Quantum Number^2*pi^2*[hP]^2)/(2*Mass of Particle*Potential Well Length^2)
E_n = (n^2*pi^2*[hP]^2)/(2*M*L^2)
This formula uses 2 Constants, 4 Variables

Constants Used

[hP] - Planck constant Value Taken As 6.626070040E-34
pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Variables Used

Energy in Quantum State - (Measured in Joule) - Energy in Quantum State refers to the total energy associated with a particular state of a quantum system. It represents the amount of energy that the system possesses in that specific state.
Quantum Number - Quantum Number is a numerical value that describes a particular aspect of the quantum state of a physical system.
Mass of Particle - (Measured in Kilogram) - Mass of Particle is defined as the total mass of the considered particle.
Potential Well Length - Potential Well length is the distance from electron where potential well length is equal to infinite.

STEP 1: Convert Input(s) to Base Unit

Quantum Number: 2 --> No Conversion Required
Mass of Particle: 1.34E-05 Kilogram --> 1.34E-05 Kilogram No Conversion Required
Potential Well Length: 7E-10 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

E_n = (n^2*pi^2*[hP]^2)/(2*M*L^2) --> (2^2*pi^2*[hP]^2)/(2*1.34E-05*7E-10^2)

Evaluating ... ...

E_n = 1.31989962995554E-42

STEP 3: Convert Result to Output's Unit

1.31989962995554E-42 Joule -->8.23816193901293E-24 Electron-Volt (Check conversion here)

FINAL ANSWER

8.23816193901293E-24 ≈ 8.2E-24 Electron-Volt <-- Energy in Quantum State

(Calculation completed in 00.004 seconds)

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Created by Shobhit Dimri

Bipin Tripathi Kumaon Institute of Technology (BTKIT), Dwarahat

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Verified by Urvi Rathod

Vishwakarma Government Engineering College (VGEC), Ahmedabad

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< 18 Electrons & Holes Calculators

Phi-dependent Wave Function

Go Φ Dependent Wave Function = (1/sqrt(2*pi))*(exp(Wave Quantum Number*Wave Function Angle))

Order of Diffraction

Go Order of Diffraction = (2*Grafting Space*sin(Incident Angle))/Wavelength of Ray

Radius of Nth Orbit of Electron

Go Radius of nth Orbit of Electron = ([Coulomb]*Quantum Number^2*[hP]^2)/(Mass of Particle*[Charge-e]^2)

AC Conductance

Go AC Conductance = ([Charge-e]/([BoltZ]*Temperature))*Electric Current

Quantum State

Go Energy in Quantum State = (Quantum Number^2*pi^2*[hP]^2)/(2*Mass of Particle*Potential Well Length^2)

Hole Component

Go Hole Component = Electron Component*Emitter Injection Efficiency/(1-Emitter Injection Efficiency)

Electron Flux Density

Go Electron Flux Density = (Mean Free Path Electron/(2*Time))*Difference in Electron Concentration

Mean Free Path

Go Mean Free Path Electron = (Electron Flux Density/(Difference in Electron Concentration))*2*Time

Electron Component

Go Electron Component = ((Hole Component)/Emitter Injection Efficiency)-Hole Component

Difference in Electron Concentration

Go Difference in Electron Concentration = Electron Concentration 1-Electron Concentration 2

Electron Multiplication

Go Electron Multiplication = Number of Electron Out of Region/Number of Electron in Region

Electron Out of Region

Go Number of Electron Out of Region = Electron Multiplication*Number of Electron in Region

Electron in Region

Go Number of Electron in Region = Number of Electron Out of Region/Electron Multiplication

Total Carrier Current Density

Go Total Carrier Current Density = Electron Current Density+Hole Current Density

Electron Current Density

Go Electron Current Density = Total Carrier Current Density-Hole Current Density

Hole Current Density

Go Hole Current Density = Total Carrier Current Density-Electron Current Density

Mean Time Spend by Hole

Go Mean Time Spend by Hole = Optical Generation Rate*Majority Carrier Decay

Wave Function Amplitude

Go Amplitude of Wave Function = sqrt(2/Potential Well Length)

< 15 Semiconductor Carriers Calculators

Intrinsic Carrier Concentration

Go Intrinsic Carrier Concentration = sqrt(Effective Density of State in Valence Band*Effective Density of State in Conduction Band)*exp(-Energy Gap/(2*[BoltZ]*Temperature))

Carrier Lifetime

Go Carrier Lifetime = 1/(Proportionality for Recombination*(Holes Concentration in Valance Band+Electron Concentration in Conduction Band))

Radius of Nth Orbit of Electron

Go Radius of nth Orbit of Electron = ([Coulomb]*Quantum Number^2*[hP]^2)/(Mass of Particle*[Charge-e]^2)

Quantum State

Go Energy in Quantum State = (Quantum Number^2*pi^2*[hP]^2)/(2*Mass of Particle*Potential Well Length^2)

Electron Flux Density

Go Electron Flux Density = (Mean Free Path Electron/(2*Time))*Difference in Electron Concentration

Fermi Function

Go Fermi Function = Electron Concentration in Conduction Band/Effective Density of State in Conduction Band

Effective Density State in Valence Band

Go Effective Density of State in Valence Band = Holes Concentration in Valance Band/(1-Fermi Function)

Distribution Coefficient

Go Distribution Coefficient = Impurity Concentration in Solid/Impurity Concentration in Liquid

Electron Multiplication

Go Electron Multiplication = Number of Electron Out of Region/Number of Electron in Region

Excess Carrier Concentration

Go Excess Carrier Concentration = Optical Generation Rate*Recombination Lifetime

Electron Current Density

Go Electron Current Density = Total Carrier Current Density-Hole Current Density

Hole Current Density

Go Hole Current Density = Total Carrier Current Density-Electron Current Density

Mean Time Spend by Hole

Go Mean Time Spend by Hole = Optical Generation Rate*Majority Carrier Decay

Photoelectron Energy

Go Photoelectron Energy = [hP]*Frequency of Incident Light

Conduction Band Energy

Go Conduction Band Energy = Energy Gap+Valence Band Energy

Quantum State Formula

Energy in Quantum State = (Quantum Number^2*pi^2*[hP]^2)/(2*Mass of Particle*Potential Well Length^2)
E_n = (n^2*pi^2*[hP]^2)/(2*M*L^2)

What is the difference between PMF and PDF?

Probability mass functions (pmf) are used to describe discrete probability distributions. While probability density functions (pdf) are used to describe continuous probability distributions.

How to Calculate Quantum State?

Quantum State calculator uses Energy in Quantum State = (Quantum Number^2*pi^2*[hP]^2)/(2*Mass of Particle*Potential Well Length^2) to calculate the Energy in Quantum State, Quantum State refers to the complete description of a quantum system. It contains all the relevant information about the system, including its observable properties, such as position, momentum, energy, and other physical quantities. Energy in Quantum State is denoted by E_n symbol.

How to calculate Quantum State using this online calculator? To use this online calculator for Quantum State, enter Quantum Number (n), Mass of Particle (M) & Potential Well Length (L) and hit the calculate button. Here is how the Quantum State calculation can be explained with given input values -> 5.1E-5 = (2^2*pi^2*[hP]^2)/(2*1.34E-05*7E-10^2).

FAQ

What is Quantum State?

Quantum State refers to the complete description of a quantum system. It contains all the relevant information about the system, including its observable properties, such as position, momentum, energy, and other physical quantities and is represented as E_n = (n^2*pi^2*[hP]^2)/(2*M*L^2) or Energy in Quantum State = (Quantum Number^2*pi^2*[hP]^2)/(2*Mass of Particle*Potential Well Length^2). Quantum Number is a numerical value that describes a particular aspect of the quantum state of a physical system, Mass of Particle is defined as the total mass of the considered particle & Potential Well length is the distance from electron where potential well length is equal to infinite.

How to calculate Quantum State?

Quantum State refers to the complete description of a quantum system. It contains all the relevant information about the system, including its observable properties, such as position, momentum, energy, and other physical quantities is calculated using Energy in Quantum State = (Quantum Number^2*pi^2*[hP]^2)/(2*Mass of Particle*Potential Well Length^2). To calculate Quantum State, you need Quantum Number (n), Mass of Particle (M) & Potential Well Length (L). With our tool, you need to enter the respective value for Quantum Number, Mass of Particle & Potential Well Length and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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