Zero Point Energy of Particle in 1D SHO Calculator

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✖Angular Frequency of Oscillator is the angular displacement of any element of the wave per unit of time or the rate of change of the phase of the waveform.ⓘ Angular Frequency of Oscillator [ω]

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✖Zero Point Energy of 1D SHO is the minimum possible energy that an oscillator can possess.ⓘ Zero Point Energy of Particle in 1D SHO [Z.P.E]

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Formula

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Zero Point Energy of Particle in 1D SHO

Formula

`"Z.P.E" = 0.5*"[h-]"*"ω"`

Example

`"5.5E^-16eV"=0.5*"[h-]"*"1.666rad/s"`

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Zero Point Energy of Particle in 1D SHO Solution

STEP 0: Pre-Calculation Summary

Formula Used

Zero Point Energy of 1D SHO = 0.5*[h-]*Angular Frequency of Oscillator
Z.P.E = 0.5*[h-]*ω
This formula uses 1 Constants, 2 Variables

Constants Used

[h-] - Reduced Planck constant Value Taken As 1.054571817E-34

Variables Used

Zero Point Energy of 1D SHO - (Measured in Joule) - Zero Point Energy of 1D SHO is the minimum possible energy that an oscillator can possess.
Angular Frequency of Oscillator - (Measured in Radian per Second) - Angular Frequency of Oscillator is the angular displacement of any element of the wave per unit of time or the rate of change of the phase of the waveform.

STEP 1: Convert Input(s) to Base Unit

Angular Frequency of Oscillator: 1.666 Radian per Second --> 1.666 Radian per Second No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

Z.P.E = 0.5*[h-]*ω --> 0.5*[h-]*1.666

Evaluating ... ...

Z.P.E = 8.78458309515881E-35

STEP 3: Convert Result to Output's Unit

8.78458309515881E-35 Joule -->5.48290312855617E-16 Electron-Volt (Check conversion here)

FINAL ANSWER

5.48290312855617E-16 ≈ 5.5E-16 Electron-Volt <-- Zero Point Energy of 1D SHO

(Calculation completed in 00.004 seconds)

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Energy Eigen Values for 3D SHO

Go Energy Eigen Values of 3D SHO = (Energy Levels of 3D Oscillator along X axis+Energy Levels of 3D Oscillator along Y axis+Energy Levels of 3D Oscillator along Z axis+1.5)*[h-]*Angular Frequency of Oscillator

Energy Eigen Values for 2D SHO

Go Energy Eigen Values of 2D SHO = (Energy Levels of 2D Oscillator along X axis+Energy Levels of 2D Oscillator along Y axis+1)*[h-]*Angular Frequency of Oscillator

Energy Eigen Values for 1D SHO

Go Energy Eigen Values of 1D SHO = (Energy Levels of 1D Oscillator+0.5)*([h-])*(Angular Frequency of Oscillator)

Restoring Force of Diatomic Vibrating Molecule

Go Restoring Force of Vibrating Diatomic Molecule = -(Force Constant of Vibrating Molecule*Displacement of Vibrating Atoms)

Potential Energy of Vibrating Atom

Go Potential Energy of Vibrating Atom = 0.5*(Force Constant of Vibrating Molecule*(Displacement of Vibrating Atoms)^2)

Zero Point Energy of Particle in 2D SHO

Go Zero Point Energy of Particle in 2D SHO = [h-]*Angular Frequency of Oscillator

Zero Point Energy of Particle in 1D SHO

Go Zero Point Energy of 1D SHO = 0.5*[h-]*Angular Frequency of Oscillator

Zero Point Energy of Particle in 3D SHO

Go Zero Point Energy of 3D SHO = 1.5*[h-]*Angular Frequency of Oscillator

Zero Point Energy of Particle in 1D SHO Formula

Zero Point Energy of 1D SHO = 0.5*[h-]*Angular Frequency of Oscillator
Z.P.E = 0.5*[h-]*ω

Why the zero point energy of oscillator is not zero ?

The lowest achievable energy (the energy of the n = 0 state, called the ground state) is not equal to the minimum of the potential well, but ħω/2 above it; this is called zero-point energy. Because of the zero-point energy, the position and momentum of the oscillator in the ground state are not fixed (as they would be in a classical oscillator), but have a small range of variance, in accordance with the Heisenberg uncertainty principle.

How to Calculate Zero Point Energy of Particle in 1D SHO?

Zero Point Energy of Particle in 1D SHO calculator uses Zero Point Energy of 1D SHO = 0.5*[h-]*Angular Frequency of Oscillator to calculate the Zero Point Energy of 1D SHO, The Zero Point Energy of Particle in 1D SHO formula is defined as the minimum possible energy that an oscillator can possess. Zero Point Energy of 1D SHO is denoted by Z.P.E symbol.

How to calculate Zero Point Energy of Particle in 1D SHO using this online calculator? To use this online calculator for Zero Point Energy of Particle in 1D SHO, enter Angular Frequency of Oscillator (ω) and hit the calculate button. Here is how the Zero Point Energy of Particle in 1D SHO calculation can be explained with given input values -> 3422.157 = 0.5*[h-]*1.666.

FAQ

What is Zero Point Energy of Particle in 1D SHO?

The Zero Point Energy of Particle in 1D SHO formula is defined as the minimum possible energy that an oscillator can possess and is represented as Z.P.E = 0.5*[h-]*ω or Zero Point Energy of 1D SHO = 0.5*[h-]*Angular Frequency of Oscillator. Angular Frequency of Oscillator is the angular displacement of any element of the wave per unit of time or the rate of change of the phase of the waveform.

How to calculate Zero Point Energy of Particle in 1D SHO?

The Zero Point Energy of Particle in 1D SHO formula is defined as the minimum possible energy that an oscillator can possess is calculated using Zero Point Energy of 1D SHO = 0.5*[h-]*Angular Frequency of Oscillator. To calculate Zero Point Energy of Particle in 1D SHO, you need Angular Frequency of Oscillator (ω). With our tool, you need to enter the respective value for Angular Frequency of Oscillator 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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