Quantum Tunneling Probability Calculator
Introduction to quantum tunneling probability
In a rectangular-barrier tunneling problem, the real work is not just entering numbers; it is choosing the particle mass, energy, barrier height, and width that actually describe the barrier you want to study. This calculator converts that setup into a repeatable estimate of transmission probability, making it easier to compare how readily a wavefunction crosses one barrier versus another.
A useful quantum tunneling calculator should make the physics easy to audit. The notes here spell out the units, the rectangular-barrier assumptions, and the point where the model changes from sub-barrier tunneling to above-barrier transmission. With that context, two people can enter the same values and still understand why the probability landed where it did.
The sections below explain what this quantum tunneling calculator answers, how to choose values, how to sanity-check the result, and which limits matter most before you trust the output.
What quantum tunneling problem does this calculator solve?
The question behind Quantum Tunneling Probability Calculator is whether a particle with a given mass and energy can make it through a finite rectangular barrier, and how that probability changes as the barrier gets taller or wider. In practice, the output helps you compare one barrier setup against another instead of guessing which combination is more transparent to the wavefunction.
Before you start, describe the tunneling situation in one sentence. For example: “How likely is transmission through this barrier?”, “What happens if I make the barrier thinner?”, “How much does a heavier particle suppress tunneling?”, or “Is the particle above or below the barrier height?” A clear question makes it easier to choose the correct inputs and know whether the calculator matches your setup.
How to use this quantum tunneling calculator
This quantum tunneling calculator works best when you treat the four fields as a matched set: mass, energy, barrier height, and barrier width all describe the same barrier event.
- Enter Particle mass (multiples of electron mass m e ) with the unit shown beside the field.
- Enter Particle energy (eV) with the unit shown beside the field.
- Enter Barrier height V 0 (eV) with the unit shown beside the field.
- Enter Barrier width (nm) with the unit shown beside the field.
- Run the calculation to refresh the tunneling probability.
- Check the output's unit, order of magnitude, and direction before comparing barrier scenarios.
If you are comparing barrier designs, jot down the four inputs so you can reproduce the tunneling estimate later.
Quantum tunneling inputs: how to pick realistic values
The calculator’s form collects the four quantities that shape tunneling probability through a rectangular barrier, so it helps to think about the barrier, the particle, and the units together before you click calculate. Many mistakes come from mixing units—especially electron-volts versus joules, or nanometers versus meters—or from using values that do not belong to the barrier regime you are trying to model. Use the checklist below to keep the setup physically consistent as you enter each value:
- Units: confirm the unit shown next to the input and keep the particle and barrier quantities in one consistent system.
- Ranges: if an input has a minimum or maximum, keep it within the model’s safe operating range for the rectangular barrier approximation.
- Defaults: any prefilled values are placeholders; replace them with your own tunneling scenario before trusting the output.
- Consistency: if two inputs describe related quantities, make sure the particle energy, barrier height, and barrier width do not contradict one another.
Common inputs for tools like Quantum Tunneling Probability Calculator include:
- Particle mass (multiples of electron mass m e ): the mass of the particle whose wavefunction is trying to cross the barrier.
- Particle energy (eV): the incident kinetic energy in eV.
- Barrier height V 0 (eV): the potential energy step that defines how hard the barrier is to penetrate.
- Barrier width (nm): the physical thickness of the barrier in nanometers.
If a value is uncertain, it is often better to run a low and a high estimate. Tunneling probability can change dramatically with small changes in mass or width, so a bracketed range is more informative than a single overconfident number.
Quantum tunneling formulas: how the rectangular barrier model is evaluated
This calculator follows the standard one-dimensional barrier workflow: gather the inputs, convert them into consistent units, evaluate the rectangular-barrier expression, and present the transmission probability in a readable form. Because tunneling is highly sensitive to energy and width, even small input changes can produce a very different probability.
For the rectangular-barrier model, the transmission probability can be written as a function of particle mass, particle energy, barrier height, and barrier width:
A common special case is the comparison between a particle below the barrier and one above it; the calculator uses different branches because sub-barrier tunneling is exponentially suppressed while above-barrier transmission oscillates with barrier strength.
In this context, any weighting term stands in for conversion factors or model adjustments rather than a generic “importance” score. For tunneling, the key idea is that width, mass, and energy do not contribute linearly: wider or heavier barriers suppress transmission quickly, while higher particle energy increases it. If the probability is not changing the way you expect, revisit the units first and then the barrier assumptions.
Worked example: quantum tunneling through a 5 eV barrier
Here is a concrete rectangular-barrier quantum tunneling example using the same inputs this calculator accepts.
- Particle mass (multiples of electron mass m e ): 1
- Particle energy (eV): 2
- Barrier height V 0 (eV): 5
A quick arithmetic check on the example inputs is:
Sanity-check total: 1 + 2 + 5 = 8
After you click calculate, compare the transmission probability with the barrier you expected to be relatively transparent or opaque. If the number seems surprising, check whether the barrier height and particle energy were entered in the same units, and then test a thinner or lower barrier to confirm the direction of change.
Quantum tunneling sensitivity table: how particle mass changes transmission
The table below changes only Particle mass (multiples of electron mass m e ) while keeping the other example values constant, so you can see how strongly the quantum tunneling estimate reacts to mass alone. The “scenario total” here is only a comparison marker, not a physical tunneling quantity, so you can see how sensitive the setup is at a glance.
| Scenario | Particle mass (multiples of electron mass m e ) | Other inputs | Scenario total (comparison metric) | Interpretation |
|---|---|---|---|---|
| Conservative (-20%) | 0.8 | Unchanged | 7.8 | Lower inputs typically reduce the output or requirement, depending on the model. |
| Baseline | 1 | Unchanged | 8 | This is the baseline case to compare against the other scenarios. |
| Aggressive (+20%) | 1.2 | Unchanged | 8.2 | Higher inputs typically increase the output or cost/risk in proportional models. |
Use the calculator's actual transmission result with conservative, baseline, and aggressive assumptions to see how much the tunneling probability moves when the particle mass changes.
How to interpret the quantum tunneling probability
In a rectangular-barrier calculation, the reported probability is the chance that the particle reaches the far side of the barrier under the assumptions of this model. Values near 1 mean the barrier is easy to cross in the chosen setup; values near 0 mean the particle is strongly suppressed and reflection dominates.
When relevant, a CSV download option gives you a portable record of the exact tunneling scenario you just evaluated. Saving that file helps you compare multiple barrier widths or energies, share assumptions with colleagues, and reproduce the same probability later without re-entering the inputs.
Quantum tunneling limitations and assumptions
No quantum tunneling calculator can capture every microscopic detail. This tool keeps the rectangular barrier model practical: enough physics to be useful, but not so much complexity that it becomes unwieldy. Keep these limitations in mind when you use the probability:
- Input interpretation: read each input label literally; changing the meaning of mass, energy, or barrier dimensions changes the transmission estimate.
- Unit conversions: convert source data carefully before entering values, especially when moving between eV, joules, nanometers, and meters.
- Linearity: quick estimators often assume clean model branches; real systems can introduce structure, interference, or non-ideal barriers.
- Rounding: displayed probabilities may be rounded; small differences are normal.
- Missing factors: surface effects, barrier shape variations, and other quantum corrections may not be represented.
If you use the output for research, safety, medical, legal, or financial decisions, treat it as a starting estimate and verify it against authoritative sources. The best use of this calculator is to make the tunneling assumptions explicit so you can see which inputs drive the probability and explain the result clearly.